Turns out the relay is good. It was the relay plug that failed. Or, anyway, one spade connection.
Here's the relay as I pulled it out. 40 amps ought to be plenty.
You can see the 30 pin got hot.
I went ahead and popped it apart since I'd never looked inside one before. 
I mean, what's not to like?
I already knew I had the same condition as when I swapped that relay in a couple months ago. No lows, only highs. So, like last time, I switched the low beam relay to the high circuit. This time it worked!
Took a closer look at the plug housing.
Well now. Hmmm.
My best guess for now: when I put the "new" relay in, it pushed the spade on that jumper wire out of the socket. Not all the way, just enough so contact became tenuous. And then it commenced to arcing.
No sound, no smell. Just heat. No problem for a 15 minute test run, at least at first. ...
I pushed the rest of the wires out, then cut the melty one and soldered on a new spade end. 
Tomorrow I'll hook up both relays without the plug casing and test to see if there's any heat still. Then I'll check the connections at the lights themselves, and trace to make sure I did indeed fuse this circuit correctly (which I think probably not, given the situation). If not it shouldn't be impossible to rearrange it so the circuits are properly fused via the panel, and if that's too hard I'll just do inline ones. Maybe I can get fuses built into the new relay plug.