First point is that the schools don't care tuppence about the aircraft that you've flown in the past. The airlines won't be particularly bothered about which light single you've flown. The only rider to this is that you may wish to fly an aircraft with sufficient kit to become proficient with NDB, VORs, ILS etc.
Second point is that the reason that CPL instruction costs more is that the instructor has spent more money to gain required licences to instruct advanced students. If you'd invested in an MEIR, for example, you'd expect to be paid more than someone who has an FI(R) and nothing more.