So the one recommendation I would make to that is potentially adding the rye first, and then the Alpha. Most enzyme manufacturers recommend adding enzymes when grains are in vs just into water.
Are you adding anything to help liquify the mash like Beta-Glucanase? Sometimes the "gummy" character of the rye causes issues.
Also just a question about the grain removal, is there a reason why you aren't distilling on the grain? I imagine lautering that must be a nightmare.
Its strange that you are running into an issue like this with the FG dropping all the way down, so its likely not sugars.
If I had to guess, it would imagine its the beta-glucans that are causing your issue. Next batch try adding some Beta-glucanase and see if that clears things up.