A calculation for winding every 12 hours :-
Weight would descent by 1+2+3+4+5+6+7+8+9+10+11+12 = 78 times the amount for one strike (revolution of the big wheel).
Distance from bottom of hood/clockface to floor = 1.3m, less height of weight and pulley of 200mm give 1m clear so 2m travel of the cord.
Amount of cord for one strike = 2000/78 = 25.64mm
If this were on the same shaft as the strike wheel the drum diameter would be 25.64/π = 8.16mm - which is far too small.
With a 4:1 gearing from the strike shaft this would become 32.7mm. 5:1 gives 40.8mm - better.
78 factorises into 2x3x13 so at 6:1 the drum would turn 13 times to wind up the strike system giving a 50mm diameter drum. Seems OK.
I will have a lever pushing the pendulum every 2 seconds and I think it could be used to wind up the strike mechanism. This could take half an hour or more giving up to 30x30 = 900 strokes.