iPhone 5S Blue Screen of Death: seemingly no options left, any ideas?

Purchased my iPhone 5S in Nov 2013, haven't had any problems until mid-December. Made the jump from iOS 7.? to iOS 8.1.2. Afterwards, I started noticing that when I would plug the phone into any cable that it wouldn't sense a charge, would need to remove and re-seat. Phone started thinking Apple cables were uncertified, things like that. No big deal, I would just unplug and re-plug a few times until it recognized the cable was legit. Note: I own several Apple and Apple-certified cables, it didn't matter which cable I used, this issue persisted across all of them.

Forward a few weeks after the update, I wake up one morning and start using my phone and it freezes. Few seconds later, the screen goes blue, several striped lines dissolve in an out between blue/gold/black/silver/white. Press home+sleep button and restart the phone, normal boot for a few seconds until it kernel panics again. Repeat about 5 times until the phone actually starts. I have my MacBook Pro, plug it in, make several attempts to backup until it works (with several kernel panics in between). Restore iPhone from backup. Issue persists. Assume backup is corrupt. Restore phone to factory settings (sacrificing all data, but I just want a working phone at this point). Issue persists. Holidays over, get back to my home.

Make appointment at Apple Store, tech takes a look at it. Notes no physical damage, no water damage. Pulls up diagnostics, everything looks good. Finds dozens of kernel panics logged, blames hardware based on the diagnostics. Tech notes that my phone is "2 months" (more like 5 weeks) out of warranty, no AppleCare, tells me they can't do a warranty replacement. Phone needs to be replaced, offers $269 for a replacement 5S. Mention the phone was working fine before the update. Tech says that sometimes the updates will cause a phone with failing hardware to finally fail (paraphrasing). Can't afford the $269, ask about upgrade eligibility. Tech passes me off to a salesperson who says I'm not eligible until November. Could sign up for AT&T Next, which as I understand splits the cost of a new phone over a year (additional ~$50/mo for a new phone?). Getting married at the end of the year, so money is tight.

Take phone to work yesterday, delete all of my apps from my phone. Plug phone into computer at work (never synced to this machine). Tell machine to do a factory reset, assume that it will be the "cleanest" sync since the app data isn't on this machine. Phone works great... for 18 hours. Wake up this morning, load up Find Friends, freezes and BSODs.

So, looking for any options outside of having to pay $269 for a new phone. Soapbox... Owned Apple stuff all my life: Apple IIe, Mac 2C, Performa 575, PowerMac 6500, iMac, iMac DV, G4, MacBook Pro (LED), MacBook Pro (retina), gen-1 iPod, iPod classic, iPhone 3G, iPhone 4, iPhone 5S. I've given the company a lot of money over my life. Rarely have I turned to them for repairs and this is the first time they've spurned me weeks outside of warranty coverage. Considering this entire thing started with an update they pushed to my phone, I'm pretty disappointed with them right now.

tl;dr iPhone 5S kernel panics and blue-screens frequently (~dozen times a day) after iOS 8.1.2 update. Few weeks out of warranty, so Apple store told me I can pay them $269 for a refurb, otherwise not helpful. Not eligible for upgrade until November. No physical damage (water or otherwise). Tried to restore from backup, issues persisted. Deleted all of my apps, tried factory restore, issues persist. Any further options?