I have a HH and a Schulz (very similiar). They are pretty much my favorite longbows. I have also tried others but prefer a d-shaped or very slight reflex/deflex longbow. The more radical types of shaped longbows really don't suit me very well.
I'd also consider other's advice on perhaps getting to a shoot and try a few used bows out. Most of the bigger shoots also have seminars and all the equipment needed to build selfbows. I think this year, I'm going to build one for myself. Last year we built one for my sonand it was a great experience. Be prepared though, it took us about 10-12 hours to build one.
Asfar as eye dominance, if you have not shotfor a very long time, I'd suggest shooting lefty.My son is a righty, but is left eye dominant. He started out shooting righty, but moved tolefty. It didn't take all that long for him to make the change over.
I believe that Howard Hill was another cross dominant shooter.If you can not make the change possible, then I wouldnt worry too much.

FWIW,at one time I inquired to Craig (he is the bowyer at HH archery) about making a double shelfed bow. He said he could do it on a new bow, but he could not modify an existing bow. If you did that, you could shoot either righty or lefty with the same bow.