All the tabs are now fully welded. Unfortunately, the drum warped a little - it's now approximately 2 mm or in the centre.
I made some brackets so I could clamp the drum to my heavy steel bench and spin it to test it's balance.
From the first rough test it's not great. Based on the battery drill rating I reckon it's getting to a bit under 1,500 rpm and shaking the bench quite a bit. It will need to be able to operate at about 3,000 rpm.
I tried again after adding a couple of bolts opposite the heavy side based on a static balance. The problem with the static balance is that I can't tell where along the length the weight is needed. I think it did improve a little, but there's still a way to go.
I'll drop in at a place near home that makes, repairs and balances drive shafts - hoping that they might do a dynamic balance for me.
I might try to press the drum straight and maybe try a better static balance by resting the shaft at each end on a couple of horizontal bars. But this still won't be as good as a property dynamic balance.
I'm keen to hear any suggestions you may have.