[X] A Long-Range Science Ship (Project Intrepid)
Hmmm, interesting.
The canon Akira seems to be a seriously solid combatant as well as a good general-purpose starship, and I think we could manage to hit that bar and maybe exceed it a little. It's the obvious safe option and is similar to the other projects we've chosen. The Intrepid program produced Voyager, a thoroughly excellent ship essentially capable of performing the explorer role in a smaller package. It would be neat to do that one given that it's our first chance to design a "protagonist" ship, and we could try and help them to be even better-equipped to help survive in the Delta Quadrant. That being said, the canon Intrepid seems very capable to begin with. We've also got recent practice building an oval saucer. On balance I think I'll vote Intrepid.
The Prometheus... is honestly sort of insane, the project appears to have produced a prototype that was capable of fighting an entire Romulan task force by itself. Not even in a "plucky ship against desperate odds" sort of way, those D'deridex class cruisers were getting trained. Absolutely rained on, like a plucky of teens from an 80s movie who decided to get into the ring and try to fight 90s Mike Tyson after he was told they had personally shot one of his tigers. It was like watching squirrels being thrown to a wolverine on bath salts.
When Starfleet sent a task group including two Defiant class ships to go and chase it down, they fared a little better, but the Prometheus still got the better of the engagement. So honestly I would suggest we leave the Prometheus alone, because the only way I can explain it is that they took every possible prototype and then lucked out so hard on the prototyping rolls that the twelve Olympians manifested in Beta Antares Shipyards and helped to forge the ship from the divine sky-iron of the gods. We probably can't realistically beat that level of performance, and altering the timeline will just make a worse ship.
Seriously, the canon Prometheus could arguably handle a Borg Sphere by itself, it's just absurd. Cruel and unusual. The Hobus supernova was actually the result of the sheer psychic backlash and impotent rage when the Romulan Senate learnt that Starfleet was planning an initial run of twelve vessels.
We cannot possibly top that level of performance, so... let's leave it well alone.