Hey man, No offense, but in my experience is this:
OMG. cook with a towel. ugh....
I have seen SOO many xbox360s that have had this done, plus various other quick fixes, come to me not to be repaired ever again.
Why? there are plastic supports under the GPU and CPU clamping mechanism, and they WILL melt and eventually will squeeze out and short the metal clamp against the board and its supply rails, blowing out the entire DC-DC switching supply.
I was able to fix one of these by rebuilding the DC-DC circuit, and then heatgunning off the melted/fused clamp assembly, with the loss of a few SMD 0402 caps. (hard to rework). But i managed to fix it. the 360 is a 16 layer board as well, and ive seen them short between layers from excess stress, and once that happens its game over unless you have a donor board to transplant the chips as I have done this before as well and its a royal pain in the ass.

Just my 2 cents on the "towel trick" or any other dumb tricks.
As far as doing IR reflows, Yes i can do it, and I am in the states, and it is my day job mostly. I know what im doing

As far as reballing, I dont reball unless its absolutely necessary, because reballing as actually worse than reflowing as the leaded solder balls break down more with tension than lead-free, plus reballing requires you to have a 100000% flat board. cannot budge, move, or warp within a micron. Reflow you have a little more give, little less error.
Lead free breaks down more with heat, but leaded is softer so it breaks down under tension. I just use the right flux and reflow them. make sure the balls get all nice and shiny, its good to go for a long time. What allows them to crack is there isnt enough surface tension to stop the solder from being able to rise and crack. Leaded balls, its a bad idea to have tension against it, because it will flatten and bridge. This is why PC CPUs have so much god-awful tension and extreme board warp from the heatsink. There is a reason for that..... xbox360s lack this, and thats why they fail

as far as any other reasons the solder fails, theres a vast majority and its a crapshoot to know the EXACT cause of the solder failure, but my findings if there is enough tension, it does not fail. But the solder that i have seen that does fail, only seems to be on chips that have very large thermal contrast during operation. Such as the G5 system processor running close to 90c then falling down to room temp, and fluctuates during sleep, and in the imac G5s, its a spring tension heatsink, which allows the system processor to be able to expand and has give, which results in what? cracked solder, and air pockets in the solder leading to failure. iBook G3s failed the BGA test as well, well what have we all noticed? yea it gets RED hot under the GPU. plus its not clamped, it has GIVE. and guess what, CRACK, fail....