The calipers were borrowed, so can't measure the diameter of the seatpost right now...
But it's been bugging me all afternoon (I was out, and you know how things just simmer in the back of your mind) so I went and had another look.
I opened out the top of the seatpost with a screwdriver - it *WAS* bent btw, and had another go.
Got the post in no problem, but it only went in about two and a half inches or so before refusing to go any further. So stuck my fingers in (thank goodness I have small hands) and yes, the welding on the seat stays is what's causing the obstruction. Ergo, that explains the 25.4 mm post and the shim.
It's something the calipers wouldn't have picked up, as they don't reach down that far into the seat tube.
I guess I'd be OK filing the weld back a little.