Just adding another success story!
I own a CECH-A01 since launch and it started failing in 2012 where it would shutdown in the middle of a game. I had it reballed at ps3repairshop.com (no longer in business), but the same thing happened again in 2014 so I bought a super slim and put my fat in my garage.
Fast forward to few months ago, I started reading about how the fat can be made into the ultimate retro gaming machine with CFW. I took out the old PS3 can tried using it. Yup, still YLODed less than 10 minutes into TLOU. I then came across this thread and got curious. I bought a lot of two clean but YLOD CECH-A01s on eBay, both still with the warranty sticker (so no funny business), with the intention of practicing the repair before doing it on my own console. The last time I soldered something was adding a DMS3 modchip to my PS2 in 2003.
I was too successful and was able to revive both eBay consoles. I was able to play the entire TLOU prologue on both of them with no issues at all. It's only been a day, but they seem to still be working without issues. If I'm able to fix my original console, then I'll have 3 fully functional CECH-A01s, enough to last me a lifetime of retro gaming.
For reference, here's my fix:
Replaced all the NECs with 32 capacitors. The capacitors are KEMET T520B337M2R5ATE009 from Mouser (Newark has them at a discount now). They're not cheap, but they're the closest specs to the NECs that I could find, and they were B case, so I could fit on the board without having to put them at an angle. They're 330uF/2.5V/9mOhms.
Bridged with 2 wires only using 14 gauge wire (important!)
I had some learning moments with the first PS3! I tried to replace only a few capacitors, but it didn't work until replaced all of them. Also, the first time I bridged it, I used 22 gauge wire, despite the advice in previous posts. It booted up for 10 seconds and then turned off and subsequently had instant YLOD. I opened it up to see that the wire burnt up (see picture). I replaced it with 14 AWG which works now.
Anyhow, thanks for all the information!