Don't know if anyone is still following this, but I lucked out in finding yet another Beta tape from roughly the same era.
I asked the seller nicely to separate it out from the huge batch it was in. (Along with a "video rental library" Fox tape, for which I needed the unique case to replace the broken one from my '82 SW Rental Beta.) I don't need another pile of old tapes cluttering up the house again. ;)
The tape arrived yesterday, and it appears to be in very good shape. The case it came in really kept the dust out. The homemade cover seems to be a video store flyer announcing the release of SW on video back in '82. Too bad it's been cut up to fit the case.
If I don't get a hernia from hooking the Betamax back up tonight, I'll let you know what I actually find on the tape. Keep your fingers crossed!