Do it
I know this is an aging thread, but I thought I'd share some additional info, as I just did essentially this same thing to my Nexus with great results. Unfortunately, I did not see this thread before starting, if I had I would have taken baseline screen temperatures, since an increase there seems to be a concern. But, you'll see post-mod temps below.
Maybe it varies phone-to-phone, but there was NO thermal compound on the chip to start with, and it does not make contact with the metal frame directly above it. The chip is essentially insulated by air-gap, rather than sinked. Can't imagine why this was done, as it basically subjects the chip and adjacent components to very high temps, instead of subjecting the whole phone to moderate temps.
Can't see most of OP's pictures, and you may be able to guess why I couldn't take any pictures during the process, but it's really simple. There is a square indent in the frame where the main chip sits; I put a layer of thick copper foil in this to fill the air-gap. Then I put thermal compound on the main chip, as well as a thin layer on the metal shield surrounding it, as this shield contacts the frame. Also put a thin layer on the SIM holder, as this also touches the frame and may pull some heat away from other components (mostly was thinking of the flash LED when in torch mode, as it's directly opposite).
I ran Stability Test's classic test for 15 minutes to see before/after, with System Monitor running in background-process mode.
Before thermal treatment:
@5:00 - 40 successful runs
@10:00 - 74
@15:00 - 107
CPU temp leveled out at 80c pretty quickly
After Treatment:
@5:00 - 50 successful runs
@10:00 - 90
@15:00 - 131
CPU leveled out at 73c
Running Linaro kernel, so throttling is not stock. Ambient temp was 20c for both tests. According to IR thermometer, screen temp leveled out at 36c (at the top, bottom of screen is cooler) after the treatment. So, this mod results in heat being transferred to the whole phone, but the temps are not enough to damage anything, and will result in a much better environment at the main chip and surrounding components.
There you have it; ~20% increase in sustained work capacity for about 30 minutes of work. And yes, my Antutu score increased as well, but we all know we shouldn't care about that...