Hope you put aside a little cash when you brought the BMW. Sounds like it's time for a tranny rebuild. Perhaps that is why the previous owner sold the money pit.
Loss of reverse in this ZF manufactured transmission is, unfortunately, not an uncommon occurrence. The typical fault is failure of the F-Clutch actuating piston. More specifically, the inner and outer sealing rings that are molded to the inside and the outside edges of the piston. As the piston’s seals fail, the clutch pack is not compressed fully and starts to slip. This slippage causes wear to the clutch material. Eventually, the clutch pack does not have enough clamping force and friction to move the vehicle. This shows as a partial or full loss of reverse.
The “fix” is to perform a full rebuild using a master overhaul kit that includes not only the clutch plates, but the intermediate steel plates that go between each clutch plate. The reason the kit with the steel plates is recommended is due to the F-clutch being fully worn out. The original steel plates will have more wear than typical for a normal rebuild. Obviously, the F-clutch piston must be replaced as well, due to the worn-out and/or damaged seals.
Here's a link to a rebuild on the Ranger Rover forum which uses the same ZF trans.
ZF 5HP24 teardown