I am having a hard time visualizing the chin support you describe. As far as the fit goes, just make sure your mask is not too big. This is a common mistake, and fencers then end up with a mask that "rattles." (Although it is fun when you pop them with your epee, and the mesh is pushed into their nose!

)
I will offer this advice: as far as non-FIE masks go, my club has been getting them from Blade lately, and I am not impressed with them at all. They are not awful, but they are not great either.
On the other hand, the masks my club used to get from Triplette are very nice for a very reasonable price. They are made by Gajardoni, although they bear the Triplette label, and are exceptionally sturdy for the price. The fit and comfort are decent. Normally, I don't recommend Triplette for many things, but their masks are still a good value.
As for myself, I love my Leon Paul mask, and would recommend it very highly. It is FIE, however, and I do not know if their cheaper masks are as comfortable, adjustable, and durable. Ask around. Also, I have a non-FIE mask by Uhlmann for coaching. It is OK, but not as solid as the Triplette ones.
I used to have a Negrini non-FIE, and it was pretty flimsy. It only lasted a year. Avoid them.
Good luck.