Hitting a snag is just part of the fun when your building something, your ball mill is looking good now you just need a little more to get in working the way you want it to,
What I see is a very small pulley on the motor, this small surface area for the belt will not provide much friction for the belt when trying to turn the large heavy drum, the motor speed is probably so fast that the motor pulley will just spin and burn the belt (slipping at the motor pulley, which would probably burn the belt at this spot, before the large drum could begin to move), I would think the motor is strong enough to turn the drum but you do not have a large enough pulley to provide the traction.
Changing the pulley on the motor may help, but a bigger motor pulley would also change the speed provided.
If this was my project I would look at several options, changing motor pulley, and possibly adding a drum pulley on the shaft of the drum (I am assuming the drum shaft is welded to the drum), a larger motor pulley and sizing the drum pulley to give the required speed, with this you could also change the type of belt (v-belt and pulleys would provide more traction).
An option to consider is changing your motor pulley and have the motor turn a pulley on another shaft, this shaft also has a pulley on it to turn the drum (adding this intermediate shaft with two pulleys, basically like a transmission between motor and drum, the motor pulley, belt and shaft pulley for the motor can be different from the drum pulley and belt on this intermediate shaft, you could get any speed desired from choosing the pulley sizes.
I would probably also consider other options also like maybe getting a reducer gear box from an old commercial dryer, or other piece of equipment, even something like an old lawn mower transmission to give the power and speed needed, the pulley sizes can also be chosen with these to get the speed desired, also DC motors are very nice as they are easy to change the speed and you can vary the desired speed needed, they can be run from Alternating current by using diodes to get the current converted to direct current (diodes would need to be sized big enough to handle the current).
Gear chains are another option to consider you can weld gears on to sleeves for your shafts, gears and chains from an old bicycle’s (a ten-speed bicycle could give several gears to choose from)
I hope this gives you some ideas, for improving your ball mill.