I have BC RS coilovers and the bottom bracket used to raise and lower the height is stuck as well as the locking perch above it.
I tried:
- flathead screwdriver wedged in notch + hammer
- loads of anti-seize
- the included spanner wrench with a long breaker bar
- heat gun (I think aluminum expands more quickly than steel)
- strap wrench on the middle of the shock and a bar between the mounting holes on the bracket

Any other ideas?

 

Don't buy cheap coilovers? But honestly, normally you'd put a torch to it, but I'm afraid it might damage the oils within the shock. You could try a block of wood on the notch of the colar and hit it a couple times with a hammer.

 

soak it with WD40 30mins later soak it again... soak it again 30 mins later, then try it...

 

I forgot to add that to my list, but instead of wood I used a flathead screwdriver in the notch.