Can I tow this TT?

This will be our families first TT purchase and we are primarily going to be weekend warriors within the state of NC possibly SC and VA. We are tent campers now and want something we can still camp with should the weather not be the best.

I have a 2009 Chevrolet Silverado LT with a 5.3L V8
GVWR = 7000 lbs
GAWR = 3950 lbs (both front & rear axles)
Max towing capacity = 7500 lbs
Combined weight of cargo & occupants not to exceed 1507 lbs.

My truck weighs 6250 lbs with my family in it and full of fuel.


Looking at the Wildwood 26TBSS which is:
825 lb = Hitch weight
5828 lb = UVW
1987 lb = CCC

Also looking at the Wildwood 263BHXL which is:
682 lb = hitch weight
5854 lbs = UVW
1828 lb = CCC

Here is my math and how I understand what I've read on here...
7000 lbs subtract the 6250 lbs my truck weighs = 750 lbs
This 750 lbs is for hitch weight and anything else I put in the back of the truck. (also for the hitch should a add WDH)
This makes me think I'd already max out my towing capacity unless I did use a WDH to move some weight off the rear axle of the TV. Or do I need to move down to a lighter TT?

Thanks in advance for any advice...

Chad