I'm not sure whether azeotropic distillation from benzene or toluene would do the job (btw, don't worry, pTSA is VERY stable).
If it doesn't, another possibility is to dissolve the monohydrate in a suitable aprotic solvent and treat the solution with one equivalent of SOCl2. When you evaporate the solution, HCl and SO2 are lost, and you get your dry acid.
I'm sure there is a much better method though, and if there is it's patented. You may look in
www.uspto.gov.