/mʌns/ for all practical purposes is the same as /mʌnts/ because we put in a "sycophantic T" between /n/ and /s/.
Thus prince = prints.
I say /mʌnθs/, or, if you want to transcribe that sycophantic T again,
/mʌntθs/. It's a "dental T" here, however, and barely audible.
CJ