The h-form is definitely much more common based on the Bashkir signage I've seen. However, I would pull a Hrant and base shha on ч rather than h. Yes, the h-form is more appropriate for the sound it encodes, but the ч-form looks more Cyrillic and the current distribution may be influenced by the choices made by the designers of existing fonts. If your font becomes as nauseatingly ubiquitous as Lobster, you might be able to buck the trend.
The rightmost /De-cy, but with shorter teeth (move the topmost quarter-circles one step down and get rid of squares) looks to me like the real /De-cy the most.
However, I've tried the same treatment with /che-cy and /tse-cy, and their teeth (tails?) look limp. They look much better when row 0 is square and row -1 is flipped so that the sharp angle points inwards.
But this approach applied to/De-cy makes it look absolutely bloodthirsty. I guess squares in row 0 and sectors turned outwards in row 1 are the only compromise that can work for both.
The misaligned breve looks fine, to my surprise. I think even a single square over the middle column will look fine.
Could you try setting some running Cyrillic text in the latest edition of Tesserae? This would help a lot to catch any shapes that don't work that well.