Obviously, none of the Franz Joseph ships would have made it to the series as they were designed after. I'm also not actually a fan. But, knowing that many are, for fun, I was imagining a reclassification of the Federation Class to, say, a cruiser. Or a frigate even, if you want to throw in other designs like the Defender Class, which, given its size, I'd reimagine as a dreadnaught.
The Hermes never made much sense to me, being without a secondary hull "body." It looks like a nacelle "foot" Frankenstein-stitched to the saucer "head" and neck. I give some credit to the Federation for at least trying to change the saucer, but using a full Constitution saucer on the Hermes to me is like using 747 wings on a Learjet, or using a factory smokestack as a chimney for someone's house... You really wouldn't.