That slow spin-up time and hand holding the motor adds to the uniqueness of what can work well. I wonder if the router can tolerate that for long and will a 1/4" shaft for the sheave not bend causing an unmanageable (unholdable) condition.
Something like this:
230v AC9060FC 6061 | Groschopp - fixed to a hinge mount (attached to your table) that is weighted to fold away when released. Use it with a VFD with an extended ramp-up time set to not overload the motor. I think I would replace the belt with two aluminum wheels - one with a heavy-duty O-ring (acting as a tire to add friction).
I'm sure you can find a better price for a similar motor with searching. Keep the shaft size at or above 9/16 for safety and ask to make sure the motor can run at your target speed like Scruffy mentioned in post ten.