I have had the same type of Beosystem 6000 and Beovox since late 2007 as combination.
The Beovox as pointed out can have mostly developed rotten bas drivers and maybe the crossovers needs updated caps. They sound great with tight bass at any volume and can get pretty loud enough to compete with a large drum kit that is not muffled down.
Any of the Beogram 6002, 6006, 8000 and 8002 have the housing on right. 6002 is the least desirable one as it is a simplified version of the 8002. The 6006 and 8000 are the same just slightly different in the design with black buttons on the 6006. Both take the MMC20 range of cartridges.
The 6002 and 8002 takes the MMC 1-5 range of cartridges.
The volume stuck is typical and simple. Open the BM6000 and the volume problem is a belt problem. You can manually move it back. The construction of the volume is not the greatest thing and it has the tendency to get stuck.
The Beocord 6000 is the same 8000 but as with Beogram 6006 and 8000 different design with black buttons.
The belts have gone and that is simple to change. Hopefully the old ones have not turned into black mess to clean up.
Martin/Dillen here can supply belts, kits for Beograms and helpful advice on fixing everything.
The Beocord and Beomaster sounds like simple and easy to go about so if you dig the Beosystem 6000 then I can highly recommend it. You can get B&O SC60 stands for it.