It's been quiet some time since this was topical, but finally I have something to show regarding the issue.
At first, having screened other subs parameters like length to beam or volume to weight ratios, I came out with a sub being 215m/705ft long and having a 25m/82ft beam at 40.000t, with said ratios being rather close to a Typhoon, Oscar or to a lesser extant the Astute.
I first had it have one big ducted prop, but when surfaced, it might breach the surface and the prop's ends might end up turning to fast leading to cavitation. So I now put two ducted props beside each other there. Those might be supported by two real pump-jets at the top and bottom in the middle of the hull.
Additionally, there are several pumpjets perpendicular to the longitudinal axis in the nose and tail to support truns. I guess rudders might not be enough for that heavy thing. And the top of the deck must be clear of obstacles for approaching and leaving aircraft.
All that is to be powered by one A1B (?) reactor that will power the CVN-21s.
In the top of the sail is a retractable sensor package including ESM/ECM, IFF, Nav/GPS, Com, and SPY-1D radar antennas. The ship is AEGIS equipped.
In the nose is the big SONAR dome.
There are also two RAM launchers at the front and the end of the sail.
In the back to the left and right are missile magazines holding ESSM, ASROC and maybe Harpoon block III missiles. Those are tall enough to hold reserve ammo below the ready to fire missiles.
In the front bottom is a torpedo room with four tubes.
The sub is only armed for self defence and relies on escorts for fleet defence.
Those three elevators, that can only be positioned in the places were they are, take up a lot of hanger space. Though even in the back are two hanger levels, there's not much room to store aircraft or so. Because of that, I think this SSLHAN needs good SSGN support, since it doesn't really have a big punch. It really trades a lot of power for stealth.
Those SSGN escorts might then carry combos of Tomahawks, Harpoons etc.
Because of that, the sub must make extensive use of UA(C)Vs (FireScout, EagleEye), like for AEW, ASW, ISR and even strike roles.
Fitting LCACs in there for amphib landings, vehicles and AH-1Zs for attacks seems hardly possible. The sub would need to be bigger, wich would increase displacement beyond 40.000t I think.
Well, so far, just a little idea ...