Update;
I found a couple of spacers in the parts drawer.
I pulled the cassette off the DB/Trainer wheel to add a spacer, but found that the cassette on that wheel was on the outside limit; any further out and the 12t would just spin.
But I checked the Fulcrum/road wheel and it DID have a spacer. A thick one, too.
So I replaced the Fulcrum spacer with a thinner spacer. Now, based on a few work-stand cycles through the gears, the indexing works fine on both wheels with no adjustment between.