blau
3514
I've got a couple ideas for you!
I share your appreciation of the 3940 (though I've never owned one) and I also share your desire for, and difficulty in paying for, a 3970. So here are two suggestions.
The first one I own and love: a 5110 worldtime. I prefer the G, but it's great in every metal.
The second is one I've coveted for a long time, but never made the leap for: the 5100. Also great in any metal, though I lean towards the J...
Both great examples of Patek's classicism, and both available in the price range you might be willing to stomach!