I don't know if this will help but I used to have an old 4 track that also made nasty clicks when you hit record to punch in. I was able to minimise it a little by instead of hitting record, hitting pause first and then record to engage the heads and then later release the pause to start recording. That seemed to lessen the problem (but it was still there).
I always tried to avoid punching in for this reason and would just record each track from the start.
Freya
