I can see a couple of options for the mechanical system:
A solenoid rather than a motor, to operate the mallet:
The striker for a bell or gong usually needs to be "floating" so it bounces away again after a strike, otherwise it mutes the bell.
By varying the pulse duration to a solenoid you could vary the force and so how hard it nudges the striker, then the striker is "thrown" at the bowl by that impulse and can bounce back, with a spring to hold it against the solenoid when idle.
Varying a pulse time or duration is very simple with a microcontroller, as they pretty much all have internal timers.
A motor could do the same thing, but using it as a rotary solenoid in effect, directly swinging the striker & with spring return rather than continuous rotation.
A normal DC motor may not work well for that, as the brushes would be in the same area permanently, but possibly a brushless motor with one winding directly switched & the mallet mount angle set appropriately could work well?
The electronics & clock side is relatively simple, with an appropriate MCU.