4 months of iPad problems

Question

Just a report on my recent experience with Apple support on an iPad.
In May, I bought the top of the line iPad3 (64Gb + 4G). A couple of weeks later, problems started to appear, in random order.
- half of the screen started to flicker
- spontaneous reboot
- 80% of apps crashing at boot
- truckload of errors and crash reports in the logs
- iPad going into recovery mode
- apps refused to install, download refused to finish
Of course, none of this was consistent. It was sporadic, sometimes coming in clusters around 2/3 days and then disappearing for weeks.
So I called Apple, which made me do a reboot, then a reinstall from iCloud, then finally a "setup as new iPad". Nothing worked.
Shipped the iPad off to Apple, with precise description of the problems.
Got an email at 2pm on a Friday: "we got your device, it's being tested"
Second email at 5pm same day: "nothing is wrong, we are shipping it back. Be grateful we didn't charge you for the diagnostic services"
I called them and asked them how could they possibly diagnose a sporadic intermittent problem in such a short time, but of course the answer was "we don't know, we don't talk to techs, we have the right tools..." Basically "shut up and take your ipad back"
I live in Hawaii, where the nearest Apple store is 150$ and 1h flight away on a different island.
Problems kept getting worse: reboot almost every day, 2/3 times a day. Finally the idea: Make a video! Used my cellphone, and decided to videotape all the weird behaviours. Got 4 minutes of footage with reboots, flickers, crashes, and all of that.
Finally decided to travel to apple store, showed the video to the "genius" and got a brand new iPad in 5 minutes.
Now Apple: costed me an airplane ticket, and 4 months of frustration.
A few suggestions to Apple:
1- TRUST your customers. Before you dismiss their claims, try a little harder.
2- Use your own crash reports. My iPad submitted at least 150 automatic crash reports, including some very troubling CRC (memory corrupted, mostly due to faulty memory chips)

Answer 1

Many thanks for your patience and kindness.
I went looking around on my external backup and low and behold, there was an iPhoto icon with the date of August 8. I have no clue how or why it was backed up, but there it is. Eveything is there on the external disk.
1. Is there a way to move that to the computer and make it my primary iPhoto?
2. My computer is 1TB, and my external disc is only 500GB. My fault, I know. Thus, I do not thing the Time Machine could be configured as a backup.
Do you know if there is way for me to set it on Time Machine, but only back certain files, such as iPhoto, and other top priority?
Thanks.