Total trailer capacity ? 18,000 lbs
Total trailer length ? 28? ... I have a 2006 F350 DRW 6.0 diesel. What I am reading is that it caps at around 15k towing capacity.
Your GCWR is 23,500. When your dully weighs in at 8,350 wet and loaded with hitch and driver (but without the trailer tied on) then your remaining tow rating would be 15,000 gross trailer weight. But that weight limit assumes you'll be climbing mountain passes and steep hills. If you only tow that trailer from one parking spot to another around Colorado Springs, then you shouldn't have any problems with burning up the drivetrain in your PSD.
So, yeah, you can move that "house" within and around the city with your 2006 F-350 PSD with no great problems But here's what I would do:
Remove anything heavy and moveable out of the trailer. (Washer and dryer, heavy furniture, TV, etc) and move them in a utility trailer or the back of your truck after you have the trailer moved and set up. Empty the holding tanks (if any) and fresh water tank (if any). Remove the propane tanks. Maybe even move all the canned food and drinks and pots and pans and dishes on different trips than when you move the trailer. IOW, get that trailer as light as you can for the big move. Then you should have no problems moving the trailer. You could even tow it over Monument Pass towards Denver with no big problems.
For moving across town in the daytime, you won't need air bags. Air bags would be required for a heavy RV trailer that you plan to tow across the country, including some towing at night. But for moving a house trailer across town, then plan to do it in the daytime and don't worry about the headlights. A little squat in the rear suspension is no reason to spend money if you use your head, drive slow, and avoid bumpy roads.Maybe an air ride lift/towing kit dependent on time/$$$.