Epilogue - third time's the charm. Here's the freewheel/chainstay clearance:
IOW, less than the thickness of the locknut. But the chain clears. And yes, I cleaned the freewheel. And the hub. Freewheel shown is a Suntour Alpha 13-30 I bought with a 1989 Hard Rock attached to it. Perfect replacement for the original 14-30 5-speed. Cleaned up fine, shifting on the stand was bang-on, got her on the road, and..... chain skips in the two smallest cogs (13 and 15). So just to confirm it's the freewheel, I threw on a Shimano MF-Z012 (or whatever it's called) 14-28 from my '89 Fuji. No more skip, but I really wanted that 13-tooth small.
Got lucky at the co-op. Found a segregated box of freewheels marked "good quality", and hiding in there was an Accushift Plus 13-32. Slipped 'em an Abe, and shifting is now like buttah, esp. for a freewheel with such a wide range and large jumps between. So now the Hard Rock I bought, primarily for the freewheel, gets its chain-skipping freewheel back. I'm debating just swapping those two small cogs, just because, with a 28 small chainring, I don't really need a 32 (not planning on climbing stairs with it),
Now what to do with that Hard Rock.....