It is funny, people of any day and age believe that they are at the pinnacle of technology and that all that is to come is already known to us.^The problem with your plans (and every other set I've seen, so don't feel too bad) is consumables. 400+ people for 5 years requires a LOT of food, water, and air. On top of that, all the infrastructure to distribute, collect and recyle it.
at 500 liters of O2/person/day, a crew of 400 would need 200,000 liters of O2 per day.
at 2 liters of water/person/day, the same crew would require 800 liters of water just for drinking purposes/day.
at 3-4 lbs of food/person/day, a crew of 400 would require 1200-1600 lbs of food/day.
Multiply that x 365 days x 5 years.
Even if you allow for recycling (which is a must in a closed-loop life system like a starship), you are not going to get 100% reclamation. So you have to allow for that in figuring how much consumables to store. You also have to allow for reserves to cover emergencies (hull breaches, tank ruptures, etc).
And what happens if your life recycling systems break down in deep space? You're going to need to keep many days supply of consumables on hand for such a contingency, assuming NO useful reclamation.
Any way you look at it, that's an awful lot of tankage space that you've taken up stuffing crew quarters, labs, and what not into every available sq meter of deck space.
You are saying that you know what will be in a few hundred years based on what you think you know today.
Lets look at the reverse. Take the capabilities of today's submarines... how long they can stay submerged, how many crew they can support, what speeds they can run at, etc., and imagine how people of Jules Verne's era (the 1870s) would react to a description of them. They would say that fuel needs, air needs, etc. would make those abilities impossible... absolute fantasy!
A little more than a hundred years ago people would believe that things we take for granted today were unimaginable. Think about the limits that they would have set on a believable story set in the year 2009. Your limits on what could happen in the 2250s are comparable to theirs.
You think this and that would be impossible... think about all the impossibilities from a little over a hundred years ago that are possible today, and remember that we are talking about stuff that is nearly twice as far into the future.