Fuel economy can be fixed in the Audi and BMW by getting the diesel engine. The Audi diesel is a V6 rather than a four-cylinder, so it's quite quick. I'd expect either to cost more than the Lexus, though. Also, while German cars have become fairly reliable during the warranty period, if you're likely to keep this car for eight or so years they become much more iffy.
Among three-row crossovers, I like how the Acura MDX drives the best. Fuel economy is good for a vehicle its size with a conventional gas engine. And it has a lot more space inside than the others. But I don't see how you can get one with the features you require within your budget. You need the Advance trim for those features, and it lists for $57,675, about $10,000 more than the NX 300hyou say is too expensive. In it's defense, click the link and you'll see that the MDX also includes about $10,000 in additional features as configured. But do these features have much value for you?
My guess is that you looked at the price of an MDX without the feature you list as required.
It sounds like the solution is to find an NX 300h with only the features you need, essentially just the Premium Package. If you can't find one at a dealer, see if they can locate or order one. Ordering will delay delivery by perhaps six months, but it'll get you the vehicle you want at the price you want.