A common problem with the /5 is that some of the oil from the driveshaft housing leaks into the final drive. The indication of this problem is that when one removes the final drive filler plug, oil runs out. You must find, and correct, the paths that the oil follows to get into the final drive. There are 3 of them. A good BMW mechanic should know that. You should question your prospective mechanic and if he doesn't know that, hit the road. Take it to a good mechanic. You can remove the final drive and take it in without the bike.
The final drive doesn't need to have the cover taken off for this job. I would remove the cover anyway because the life of the final drive is the gear wear. I would want to inspect the gear wear and correct it if it is wrong, before you must buy the gears too. Another reason for removing the cover is that the brakes would sometimes get wet with oil. The drain hole didn't help here. The drain hole only drains oil that leaks past the seal. Check the drain hole yearly, with a wire, to see that it is clear. It is located just below the axle nut.
The higher oil level, caused by transfer, causes excessive pressure in the final drive. Then the oil leaked along the threads of the 10 studs that hold the big round cover plate. This is why the oil got onto the brakes, and was a safety issue. This was a frequent occurrence in 70-71. The big nut holding the splined gear must be removed using a special tool. The threaded ring that holds the seal must be removed using a special tool. Clean everything totally.
The three paths for oil leaking into the final drive are:
When these bikes were new, they often leaked (transferred) oil badly. We could fix one without replacing any parts. The parts weren't bad, the manufacture and assembly of the parts was less than perfect. Isn't that diplomatic? The early models in 1970 had miss-machined covers. A recessed groove was allowing oil to get to the threads. We just filled it with goop. Where I say "goop", we used Hylomar, but I hear that many modern types of goop are good. Hylomar HPF. Available at auto supply stores with the rest of the Permatex products. The Permatex part number is 25249.
I see this problem all the time. When I do the service I disassemble the final drive completely and inspect. I replace all three seals and apply "goop" as you say, in the appropriate areas to prevent leakage. Doing it right and doing the complete job at one time leads to lots of trouble free miles. On the other hand; doing half the job leads to future leakage problems that end up costing more than if you do the whole job right the first time.