Why don’t you instead allow users to have their desired input of any amount; not tied with 2 mBTC, it can be 0.00256 BTC as well. I'm not sure such things existed in ChipMixer or not; I can't remember exactly as I had checked out long ago.
If customer wants custom value of chips then chip cannot be ready before deposit unless we predict all possible sizes and create them beforehand. If they always get chip created after deposit then it is less private than getting chip created after deposit or before deposit.