ITunes Network Diags pass, but Restore fails with Error 3014 and recommended solutions risky and unhelpful

Question

We've had routine OS updates fail recently (weeks apart)
on both an iPad mini and a 5th Gen iPod. The devices ended up in recovery mode
and we had to Restore them to factory defaults.
That is bad enough, but it gets worse...
We started iTunes, plugged in the bricked device, and were
prompted to do a Restore. Clicked OK. It ran for a while, completed the
extraction step, and the failed with unknown error 3014.
We searched support, and there is plenty written about
unknown error 3014 when doing a Restore. Most point to network connectivity
issues and things like blocked ports or conflicting security software. Sure, I
can see how those could cause problems that may be outside Apple’s control
(although doing everything over HTTPS would eliminate the issue.)
BUT, iTunes has built in network diagnostics (Help ->
Run Diagnostics… -> Network connectivity tests). Shouldn’t these tell me if
there is a connectivity problem with iTunes? The support articles all seem to
tell you to manually dive into all kinds of low level  things such as hosts files.
iTunes network diagnostics all passed, but out of
desperation, we still tried shutting off our anti-virus (Avast) and firewall
(Comodo), connecting directly to the internet without our router blocking or
filtering anything, editing the hosts file, trying a different PC, etc. as
instructed. It was all a wild goose chase – nothing helped, and Apple’s
instructions exposed us to security risks (attaching directly to the Internet
with no router, firewall or ant-virus software!)
I can’t be 100% sure because I still had our anti-virus
SW and firewall turned off, but what seemed to finally work was to just try
dozens of times until iTunes and Apple’s servers finally worked!
After dozens of tries on two PCs over two days, the last
thing I did was to turn off our anti-virus and firewall again, started iTunes,
plugged in the device, attempted a Restore when prompted, retried when it
failed. Then closed and reopened iTunes while leaving the device attached, and
Restored when prompted. That one time, we got lucky and it worked. I’m sure
many people really have blocked ports, etc. but I can’t see how that could explain
our problems. Hopefully this posting will help someone.
** Apple – If you’re reading this ** Please (1) find out
why we and others in the forums report persistent 3014 errors that seem to
magically go away if you retry often enough over a long enough period of time,
and (2) make sure the iTunes network diagnostics are truly thorough, and then
direct customers to them rather than making them dig through port mapping
settings and hosts files. Thanks for your consideration.
This is a terrible user experience – Please address this!
A few of the refs I found:
http://support.apple.com/en-us/HT201413
http://support.apple.com/en-us/HT203875
http://support.apple.com/en-us/HT202944
https://discussions.apple.com/message/20645785#20645785

Answer 1

P.S.  Here is a copy of one of our update logs that iTunes optionally sends back to Apple when a failure occurs, etc. (We let several of these be sent in) There are several errors near the end, including an "Internal error"
iPodUpdater 1 2015-01-01.log
2015-01-01 21:42:12.948 [7316:1c4c]: restore library built Oct  7 2014 at 14:24:11
2015-01-01 21:42:12.948 [7316:1c4c]: iTunes: iTunes 12.0.1.26
2015-01-01 21:42:12.948 [7316:1c4c]: iTunes: Software payload version: 12B440
2015-01-01 21:42:12.948 [7316:1c4c]: iTunes: Using MobileRestore state machine
[02:42:23.0846] Changing state from '(null)' to 'Restoring'
[02:42:23.0846] requested restore behavior: Erase
[02:42:23.0861] requested restore behavior: Erase
[02:42:23.0861] requested variant: Erase
[02:42:23.0861] requested restore behavior: Erase
[02:42:24.0532] amai: _AMAuthInstallBundleCreateServerRequestDictionary: withApTicket is True
[02:42:24.0532] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "RestoreLogo" Digest = "<CFData 085DB3E0 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0548] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "RestoreDeviceTree" Digest = "<CFData 085DB938 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0548] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "RestoreKernelCache" Digest = "<CFData 085DB6B0 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0548] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "RestoreRamDisk" Digest = "<CFData 085DB308 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0548] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "iBEC" Digest = "<CFData 085DB278 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0548] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "iBSS" Digest = "<CFData 085DB350 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0548] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "KernelCache" Digest = "<CFData 085DB110 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0548] amai: _AMAuthInstallBundleCreateServerRequestDictionary: entry "ftap" not part of manifest, skipping
[02:42:24.0548] amai: _AMAuthInstallBundleCreateServerRequestDictionary: entry "rfta" not part of manifest, skipping
[02:42:24.0563] amai: _AMAuthInstallBundleCreateServerRequestDictionary: entry "ftsp" not part of manifest, skipping
[02:42:24.0563] amai: _AMAuthInstallBundleCreateServerRequestDictionary: entry "rfts" not part of manifest, skipping
[02:42:24.0563] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "BatteryCharging0" Digest = "<CFData 085DB1A0 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0563] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "BatteryLow1" Digest = "<CFData 085DB7D0 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0563] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "AppleLogo" Digest = "<CFData 085DB4B8 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0563] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "DeviceTree" Digest = "<CFData 085DB5D8 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0563] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "BatteryCharging1" Digest = "<CFData 085DB668 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0563] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "BatteryPlugin" Digest = "<CFData 085DB740 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0579] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "LLB" Digest = "<CFData 085DB428 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0579] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "iBoot" Digest = "<CFData 085DB1E8 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0579] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "BatteryFull" Digest = "<CFData 085DB470 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0579] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "RecoveryMode" Digest = "<CFData 085DB500 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0579] amai: _AMAuthInstallBundleCreateServerRequestDictionary: personalizing "BatteryLow0" Digest = "<CFData 085DB6F8 [7253907C]>{length = 20, capacity = 20, bytes = 0x<<<<<<<<<<<<<<<<<<UDID>>>>>>>>>>>>>>>>>>}"
[02:42:24.0579] amai: _AMAuthInstallBundleCreateServerRequestDictionary: using UniqueBuildID <CFData 085AD430 [7253907C]>{length = 20, capacity = 20, bytes = 0xb4a53a00140f136ddf267a31b6d37652a4452586}
[02:42:24.0579] amai: AMAuthInstallRequestSendSync: SSO function returned NULL and no SSO token was provided, SSO disabled.
[02:42:24.0704] amai: tss_submit_job: HttpEndRequest failed=12031
[02:42:24.0704] amai: AMAuthInstallRequestSendSync: failed tss submission: Internal error
[02:42:24.0704] amai: AMAuthInstallApCreatePersonalizedResponse: server request error: Internal error
[02:42:24.0704] amai: AMAuthInstallBundlePersonalizePartial: failed to create ap ticket
[02:42:24.0719] failed to personalize the restore bundle: Internal error
[02:42:24.0719] AMRAuthInstallDeletePersonalizedBundle
[02:42:24.0782] Restore completed, status:3014
[02:42:24.0782] Failure Description:
[02:42:24.0782] Depth:0 Error:Failed to copy preflight options during recovery mode restore.