We have a Bullet Premier with an island that has 2 slides that bump up against the island. I don't have an issue with it because our fridge is across from the main entrance. You can also access the bedroom, pantry and the bathroom while slides are in. I can't get to the back, but I really have no need to get back there while traveling. If I do need to get back there, I jsut put the slide out...no big deal.
I would be concerned about the weight of the trailer as well. Our is a 30' and we have a Tahoe which can pull a little more than the Suburban according to the tow weight. The issue we run into is payload. Luckily we put nothing in the truck except fuel, 2 adults and 3 dogs. We're right up against our weight limits, but not over. With a 34' trailer compared to our 30' I would think you would end up over, especially if the total weight of people/things in the truck is over 600-700lbs.
I've been eyeing up a Suburban 2500 to upgrade and hav eplenty of cushion, but the amount of use and the benefit isn't there for me right now. I'd love to find a 2500 level pickup that had enough room for 3 dogs in the crew cab, but that hasn't happened yet.
With the trip you have coming up, I think you'd be happier with a larger tow vehicle. I've driven back and forth to MD from FL and the trip is fine, but a little bumpier feeling than I'd like. I know I'd feel more comfortable with a larger tow vehicle.
You'll be right around 1000lb tongue weight which is the highest amount your hitch rating will allow, which will leave you with about 700lbs of payload.