Likely need to swap the crank and LH cam sprocket from the old engine. The tone wheels for the crank and cam sensors are part of those sprockets, and there are a couple different patterns.
Probably transfer clutches. Get them new, and fix it. You don't have to pull the transmission, and a used trans is likely to also have worn clutches.
Also inspect all rear suspension and diff bushings. AWD could be engaging normally, but a bushing is clunking when it's loaded.