So I would stick with a similar plan to your original, b/c if it was me, I'd always be like, 'dam, wish it was the other way like I planned'.
Like it is mentioned, having the HT next to bedroom really comes down to a couple of things.
If it's a guest bedroom, and won't be used on a daily/regular basis, I'd refine my sound containment strategy and move forward.
If it's a daily bedroom, then I'd again refine my sound containment strategy and provide the occupant with a lifetime supply of earplugs.
With that said, I'd change your currently planned door to a single solid core door.
I'd consider putting the screen wall on the stair side wall. This way you could build a wall that has some subwoofer cubbies, 1 in-between the sump pump and the pressure tank, and another one under the stairish location.
But additionally, you could build a closet in the corner between the bedroom door and the HT single door.
Build a riser over the sump pump in the corner with trap door for access.
Have the contractor move the HVAC lines, one to the outside wall, and the other line to the ceiling/wall adjacent to the bedroom. You could then bury it into a soffit and make it like a design feature.
I'd consider putting the screen wall on the outside wall on the right side, based on your photo, and build a stage over the top with a trap door. This would hide it, but also be accessible. It would be behind an AT screen so not to much of an issue. Since it's in the corner, I'd build a removable bass trap for easier access.
Again, single door, but this time, since you may want to have the second row of seats, if you need those, or a bar in the back, you could potentially use space under the stairs for a 19" rack location, and would be close to your server... if thats the way I read it, but keep the back row /bar away from the back wall for surround sound encompassment. Recommended is 4 feet, but I get good ambiance with 2' in my room. That may work in yours.
Still have the contractor move the HVAC lines though out towards the edges. Make it easier to encase in a soffit.
Use treated lumber on the bottom of a double sill plate.
Consider building an isolated plywood floor to allow for moisture separations from carpet to concrete. Since you have sump pumps, this would help with keeping it dry... Do not build the walls on top of this.
also, install several leak detectors.. don't want to see all your good work get soggy. Insteon makes a good one. saved my buddy allot of money..
Anyway, I definitely think you can salvage your plan.. just takes time and $$$.
Good luck and I'll be watching your build.