We maintain a C340A at Aerotech, which the owner may be willing for you to try with himself or one of the company pilots for which it is used. You can PM me if you need contact details. It is based down here at Coventry.
I have done a fair bit of flying on it getting it airworthy after it was substantially refurbished by its new owner and it is a nice machine complete with the RAM upgrade to increase the engine power plus the vortex generators enhancement and speed brakes.
That said, you could always try a C335 which is basically an unpressurised C340 and is very similar to fly. We also maintain a C335 which is based up at Leeds, which is possibly handier for you if you are Yorkshire located.
Other than that, why not do a G-INFO search on C340A and write to the owners, looks like you have only 7 showing, so not too expensive in stamps! (Coventry one is G-SAMM)
Best of luck
FF