I’ve got no connection to PSTT, but you might want to consider these three factors:
(i) the reason they have no availability until May could be that they’re booked well in advance because they’re popular.
(ii)Also, every single training provider worth their salt has a backlog of candidates due to covid restrictions, and
(iii) the availability of tests is a limiting factor for all TPs, and one which they have no control over, as this is all down to the vagaries of DVSA.