I have some very nice 15-inch unbranded drivers (subs, I think they might be Beyma but that's just a guess); they do not need re-coning per se because the voice coils move freely with no scratching; however, the surrounds are brittle and falling apart. 

Is replacing surrounds a thing? Has anyone here done it? Where could I get some from? All I have been able to find is foam rubber ones that typically go on car stereo speakers; I don't think they would be substantial enough for 'real' subs.

Yes it is especially with foam and rubber surrounds which tend to dry out and get brittle. Cloth surrounds can be replaced too but if they are intact but just weak sometime applying a fresh coat of sealer(surround dope) will refurbish them enough to negate the need to replace.