I found a "fix":
If you go to the "LIVE" part of Analog Lab, you can assign individual presets to one of 127 slots. If you put the presets you're using there, on one of the slots, and have it selected from there, you can duplicate the track, save, load, etc. and the preset will load properly. Of course the number of slots is limited, but 127 should be enough to at least keep you from manually reloading presets every time you load your most recent projects or songs.
It's a shit way of doing things, but it's better than nothing I guess.