Hi there!
That is a very specific case and I would really need more information from you. Because saying "I think I’ve set everything up correctly" does not make me know if you really did. I need to see what you did. Meaning, how did you created the bitmap font, how did you set it on the plugin parameters etc. Honestly, I never tried a game with that resolution size, 360x176.
So the best course here for me to debug this is, if you could send me through discord a sample project replicating the issue, so I can take a look and see exactly how did you make everything.
But, it is worth mentioning that, if you are looking for a pixelated font, if your game is going to the pixel perfect way, your resolution also need to be pixel perfect. Otherwise, when going fullscreen, it will get blurry. For example, if your games uses 32x32 assets:
320/32 = 10 → Ok!
176/32 = 5,5 → Not Ok for a pixel perfect game! Things can get messy.
Either way, here is my discord: hakuenstudio
Call me there and tell me you are the one with the Bitmap Font problem.
EDIT: But I may only be able to take a look at this on monday.