Is this font salvageable? If so, how?

JoannesMathieu

[nvm]

Craig Eliason

The closed "open counters" make some sense in the bold as a consequence of fattening everything up. I'd say the other two weights are dead ends. 

K Pease

I'll go further and say the closed parts look like an accident in the context of hairline spacing. So, either cut the serifs apart or design it so all the letters are meant to join and overlap.