Thanks. The strike is probably a century old. I'd have to do a lot of
work on the jamb to fit a new strike. I've fooled around and somehow
the play in the door is down from 2.5mm to .25mm. That pretty well
solves the problem.

I see the end of the latching tongue is rounded, as is the edge of the
hole in a modern strike. That would be why slop in the tongue wouldn't
matter. I don't know the nomenclature, but there's a little deadlatch
tongue and an insert in the big tongue for the little tongue to slide
against. That insert was hanging up against the square edge of the hole
in the old strike. A little filing should fix that.

DanG wrote:
If the D strike has a "tongue" inside the latch hole, it is often
used to fine tune the latch point. Just reach in with a small
screwdriver or similar and bend the tab slightly.

.1 of an inch is less than 1/8". That would seem a normal
tolerance in my opinion.