Just finished installing the new cooler, and I'm happy to report its working fine and cpu temps are much cooler. I ran a quick 20 minute game of BF4 and then Crysis 3 and at full load the highest I saw the temps go was 36c on core #2. Other, then that, its running much better. No lag at all in anything, games or otherwise.
I don't have any calipers to verify that the height of the screws matched each other. That'll be my next project, after cleaning up the rats nest that is my poor cabling job. However, I've added some pics of the new cooler installed.
Welp, I'm pretty sure this thread can be closed. Thanks again to everyone for all your advice!