ice.cold

You could try using "ME Cleaner" on a dump of your ME firmware, it might remove any cpu checking code if you're lucky. You can get the program from here: https://github.com/corna/me_cleaner and there is a guide to use it here: http://hardenedlinux.org/firmware/2016/11/17/neutralize_ME_firmware_on_sandybridge_and_ivybridge.html

That's a possibility. Have you tried flashing a stock K5000M vbios onto it? If it really is a K4000M board, then the drivers won't let the card enter the P0 clock state, with a non-matching vbios that isn't modified.

I don't think the vbios is the only thing that controls the number of active shaders; I posted earlier about crossflashing my gtx765m to a gtx770m, which didn't unlock any extra shaders. I think the chip still needs to have the shader cores enabled in the first place, otherwise the extra shaders should have been unlocked. It's strange how your screenshots only show 960 shaders for the K5000m, as the normal chip has 1344 shaders, and the gtx680 should have 1536. If it was being limited by the vbios, then it should show 1344 for the transplanted chip, not 960. I guess one way to properly test if the vbios limits the shaders is to crossflash a high-end card with a lower-end vbios and see if the shader count changes.

Very interesting that your core swap worked without having to modify anything else. Some time ago I tried flashing a 770m vbios onto a 765m MXM card. I had to edit the soft straps to match a 770m, as the drivers won't use the P0 state otherwise, but after that the card functioned just as it did before (using the lower clocks in the 770m vbios). Unfortunately it didn't unlock any extra shaders, but it does support the theory that a core swap on a newer nvidia card would work without extra modification. This also suggests that a different memory configuration (192-bit to 128-bit) might not matter either. I look forward to seeing your results with the 560ti core to 485m swap.