me three!
I especially like when a real expert (not me) comes thru with a slam-dunk positive ID, I'm generally gob-smacked!

Another thing for the OP to check: it possible that the nice Miche 27.0 seatpost is not the correct size, the clue being if the gap in the rear of the seal lug shows signs of pinching.
It wouldn't be much but possible that a 27.2 is actually the correct size IF the seatlug and seattube were properly round and smooth in the top 6" or so.

Very possible that all the frame bits are "Italian" (and maybe all GPM) but I don't know of too many Italian made frames ffom this (mid-late) 1980's era that used that modified "Dutch-style pinch bolt" on the back of the seatlug instead of a lug with conventional "ears"...plus if it's really Brit BB threading then all bets are (farther) off.

The stay caps/tips I was try to recall may have been the ones used on some Gios, but they had a more pronounced concave "scoop" to them, so that's no clue. However there were some Bianchis that MIGHT have used a cap that's more like the shape of the OP's and those that I can find in my crude image search seem to be about the same vintage BUT these have the typical "B" in a circle panto...not much help