I can't give you any tips on finding unlisted Gators. We have a 42 and are always "aware" of other Navigators in the area since they are more of a west coast boat (built in Perris, CA). What I can tell you is the 44 and 46 sizes are kinda the "oddballs" of the fleet (well, our 42 is too... we have the only example of a 42' made during our model year). Anyway, as you have probably discovered in your search, 44s and 46s are pretty rare. You might be better off to go ahead and jump on a 48 if you find a good example in your area. If memory serves (Bess, help me out here) there was recently a 44 for sale in New Bern, however, I believe it sold.
You could join the NW Navigator Yacht Owners Forum on Facebook. And yes, by the name, you would think they are all in the NW, but there are plenty of us Easties on there as well. They might be able to spot one for you.
And as a side note, I never knew the 2 versus 3 bedroom layout was even an option. I learnt me sumptin' today. YAY!
2000 Navigator 4200 Classic
(NOT a trawler)