Afaik the costar stabilizers can and do have problems with cherry profile keycaps. I've noticed it especially with GMK keycap sets. I've seen some people sand down the inside of their keycaps to fix this issue but that is probably not the best idea tbh, it seems like it takes a LOT of sanding to get it to not happen.
I have the same setup, filco mj2 in tex case, and it is starting to drive me nuts. All the stabilized keys are having big issues with GMK caps (not so much with the enjoypbt cherry profile caps I used before it seemed)
At this point I am just trying to see if I can't find the files for a replacement plate for the filco mj2 such as this:
https://geekhack.org/index.php?topic=36907.0Would be able to swap the board out to cherry stabilizers with that plate and not have to deal with this issue, but I think my chances of finding those files are pretty low.