I looked up a few things quickly on the GK61 and compared with what I know.
I would choose the denser automotive foam. Or... first reinforce the bottom of the case with lengthwise ribs of some material epoxied to the bottom, to make the case more rigid.
You could find similar automotive damping foam also in stores for car accessories.
Next, I would put rubber O-rings on the standoffs that the PCB-plate sandwich rests on. I've heard that the GK61 uses 2.5mm screws (so you'd want O-rings with 2.5mm holes), but you might want to measure that to be sure. If you can't find
thin O-rings, maybe you could punch holes in pieces of a rubber band or something.
The most effective method of damping is otherwise to use switches that are damped in the first place: such as Gateron Silent Red or Brown, Cherry MX Silent Red (also called "Pink"), or any of the several newer expensive boutique switches that are "silent" (that would probably set you back more than the whole GK61 did though). Those are not compatible with the optical version of the GK61 though.
There is a page in the Wiki about methods for
damping but it is a bit outdated, lacking many new mods from the past few years. (Note that the article also mentions other types of switches/keyboards than just Cherry MX-style.)
Among several newer mods: "PCB foam", "switch pads" (not optical), "holee mod", "band-aid mod". (You can find many instructive videos on them on Youtube)
Keyboard modding and upgrades can be a really a deep rabbit-hole to fall down through if you're not careful, and some of those mods are really not that noticeable compared to the one you have already planned.
Unfortunately, the GK61
seems to be incompatible with most "standard" 60% parts out there, such as aftermarket cases and plates, because it has standoffs in different positions.