Your ship is made to be a warship. I was told we were exploring. Common sense dictates you would want to explore in an exploration cruiser.
The ship I gave is made for long range exploration. It uses a crystalline form of dilithium, they can be recharged and reused over time. The ship uses beam arrays, beam arrays have no moving parts which means high reliability, which means you can go long periods of time without maintanence.
The ship has a lot of interior space for engineering and laboratories. The very shape of the hull is meant to increase warp and quantum slipstream efficiency, for fuel efficiency. Better fuel efficiency means longer time before refueling.
The large engineering facilities mean that the ship can repair itself.
Replicators mean that you do not need food or water storage but so long as you have energy you can replicate them.
A 500 man crew is the optimum mix between too few crewmembers and too many crewmembers.
Everything about the ship I am giving you is made to do the job at hand. My ship fits like a glove, yours is made to wage war, not to explore, we all know it.
My point is, the ship will just be the way it looks. We can make it a exploration cruiser that looks like that if we wanted to.
Well also, now I see another reason why it s not a good idea to go with mine, if people saw the Hyperion, they will think about running rather then talking. Also, that means we will have all firepower we need, which will dull the plot.
I recommend 500 crew, not including troops.