The Apollo A630/50MHz was the fastest A600 CPU board, they also made 33MHz and 28MHz(?) versions as well.
They were supposed to run without any cooling, but from experience, they all seem to get really dodgy after about 10-30 minutes running with no cooling.
Unfortunately the PLCC socket to clip onto the 68000 is the only "easy" way to upgrade the CPU. The expansion slot does not have the required control lines to run a CPU board.
The PLCC socket is not an ideal way of doing it as it tends to come loose and go intermittent over time. Find some way to fix the CPU board down somehow.
My A600 is currently fitted with an A630/33 and a small fan over the CPU. It runs well and is quite reliable.
If you need another CPU board, Graham C from Compkarori (Wellington) had a spare A630 in near new condition some time ago. Don't think he's sold it yet.