IPad 3 not showing up in iTunes (Win7_64) over WiFi

Question

I have an iPad 3 I'm trying to sync over my WLAN.  It's running iOS 7.1 and connecting to iTunes 11.2.2.3 on Windows 7 64-bit.  Upon launching iTunes, the device will appear in the left navigation pane after about 10 seconds, and will stay there (greyed out with a spinning progress wheel) for about 15-20 seconds before it disappears.  I am never able to display the status or contents of the device over a wireless connection.
-USB connections do work and I am able to manage, browse, update and sync the device.
-I have tried connecting over USB and checking/unchecking the "Sync over WiFi" box.  That has not solved the problem.
-I have tried establishing custom inbound and outbound Windows Firewall rules to allow all traffic to all programs and ports  from the iPad's internal IP (10.10.10.18 on a /8 network), but that hasn't fixed the problem.
-AppleMobileDeviceHelper.exe, AppleMobileDeviceService.exe, iCloudServices.exe, iPodService.exe, iTunesHelper.exe, iTunes.exe and mDNSResponder.exe are all running at the time of attempted (and failed) sync.
-Wireless syncing worked properly while on iOS 5.  Really regretting updating to iOS 7 right now.  Lesson learned, unlikely to ever update again.
I've tried a number of solutions but as I cannot recall 100% of what I've already tried, I am willing to start at square one to get this resolved.  For what it's worth, I'm a 14-year IT professional so you can talk to me about pinging, firewall rules, subnets (iPad and PC running iTunes are on the same subnet), protocols and ports and I will know what you're talking about.  Hope that helps speed things along.
Any assistance you can render would be most appreciated.

Answer 1

Wireless Sync
To set up Wi-Fi syncing, connect your iOS device to your computer with the included USB cable.
Click the Device button in the upper-right corner. (If viewing the iTunes Store, click the Library button first.)
If you don't see your device, choose View > Hide Sidebar.
In the Summary tab, select "Sync with this [device] over Wi-Fi."
When the computer and the iOS device are on the same network, the iOS device will appear in iTunes, and you can sync it.
The iOS device will sync automatically when the following conditions are true:
The iOS device is charging.
iTunes is open on the computer.
The iOS device and the computer are on the same Wi-Fi network.
While the iOS device is in the left-hand column of iTunes, you can select the content tabs and configure sync options.
Click Apply or Sync to sync the iOS device.