As you might have read earlier on the article about fixing a crack on the floortom, it looks like the shell is quite out of round. Well, it really is, about 6 mm (1/4") on the resonant side and 3,5 mm on the batter side.
I'm not too concerned about how a slightly out of round shell might sound bad or not, but rather about the head not fitting evenly and properly.
Here's what I did to reshape it without damaging it any further.
The idea is to secure the shell in shape by using perfectly round plywood rings, attached using the lugs mounting holes. To make fitting easier and to avoid having too much effect on vibration, the ring won't touch the shell, except at the mounting holes, through small beech dowels.
It seems to work, the diameter looks more consistent (about 2 mm variation). I can live with that, even though I was expecting less. Maybe I should design a more accurate / fine tunable construction.