I dont think the date is far enough out for the BP or the BIG INGY and it would need centre seconds too.
I quite like the new Climate action Ingy on the Gen site
My wife has that same movement in her 217 and it is very good, i think it may be a little more swiss than the e with the correct dager adjusting arm too
You might be able to limit the damage bu not using tubes or the other solution is to thin the strap at the lug end by reaming out the tube hole, i learnt this early on when i had to remake a couple of straps for a cutomer who uses DSN cases as they have shorter lugs, 47mm cases dont have this problem in general as they are rounded but all the 44mm i have seen require the lug ends quite thin to totaly avoid it.