I would say that you could replace the pressure regulator located in the valve body, it's (ZF#0501 210 060 - Pressure Regulator) it's located at page 34 - 51.260 in the ZF Parts Catalog. It could also be the pistons and parts related to that part in the valve body, depending on the condition of the valve body it may perhaps also be a good time at doing a valve body rebuild yourself...

HOWEVER having black and burnt fluid tells me the clutch packs have been slipping, most likely due to insufficient pressure to the clutch packs, which means you've most likely burnt or worn them out. Not a good sign for a healthy gearbox.

My F Clutch Pack Piston was blown and it burnt out the friction material in the clutch pack due to the slippage. I didn't want to pay the amount of money that BMW or any shop wanted to fix my transmission ($4,500 to $6, 000CAD) so I did it myself. You can have a look at my post here.

If you just replace the pressure regulator I would recommend flushing out the trans fluid, and I suppose you could just continue driving it until it does fail completely... Let me know how it goes for you!