Well, the dryer has been disassembled and vacuumed, the dead coil removed, the new coil swapped in, ready to reassemble as soon as the new belt arrives. I was surprised how much of the brown shmutz in the heater was just ash from the coils - it dusted off quite shiny after I replaced the coil.
Before
After
I'm a little worried about the visibly duller part of the heater assembly, hopefully that won't absorb too much heat - I tried to cluster the coils a bit looser there to compensate.
It's even visible on the reverse side.
Either way, I'm reassembling tomorrow when the new belt arrives.
Oh, regarding the burned spot, if the coil failed because it picked up lint, that burned on, insulated/heated up more from the lint catching fire/whatever, bending the coil outwards could actually make it more likely to catch lint/whatever. No idea with your dryer if that chance is better or worse than the possible benefits of spreading, just a thought.