I bought the Lattices a while back, but was quite reluctant to switch from the Teardrops because I worried the ride would suffer - and I liked the Teardrops. Having fitted the Lattices, I now think the car looks MILES better! I don’t find the ride has suffered either - I guess that’s the march of technology showing how old fashioned the Pirelli P4000s were. The new tyres are also much quieter with a LOT more grip.
There are two types of 16" Lattice wheels, the 8J type with an offset of 33mm used on the XJ40 and the 7J with an offset of 28.5mm used on the XJ-S. Either will fit the XJ40, but only the 7J will fit the XJ-S without a spacer (IIRC they foul at the front?) I’m sure you know this though.
I really like the 16" lattice - they’re my favourite wheel on the '40. If you can’t find a set of Lattices, those BMW wheels will look pretty good though, I would think.
**Edited. It was the DB7 I believe, although DB9 would also work as Aston shared same unique lug pattern as Jaguar… Have to look it up. The price i don’t recall, but it was very low for all 4…some deal at the time. It was even international shipping. I believe they came from Australia? It was 16yrs and a lifetime ago now.