I'm a little late to the party, but I'd say stick with what you have. You've got the king of the hill of SUV tow vehicles.
Regarding option 2 - I have a family of 5, and we never even remotely considered a pickup. That third row is invaluable. I couldn't imagine 6 on a long road trip, even in a mega cab Ram.
Regarding option 3 - The problem with a diesel Excursion is the weight of the engine, and the impact on payload. Especially the 7.3. With a family of 6, I'm thinking you need as much payload as possible, and the 2500 Suburban is the better choice.
I've towed my behemoth (8600 lbs) out West several times, including Powder River Pass (9666') and the Eisenhower Tunnel. And I only have the 6.0. The 8.1, especially with some light mods, should do everything you need it to do, even in the Rockies. Stick with it, and don't have any doubts.
Our rig, stopped at Powder River Pass, on our way to Yellowstone: