Nash would be another one to consider. They use their own in-house built, heavy duty, off-road frame which Nash also provides to Outdoors RV for all their TTs. Both brands are owned by the same company. The frames are in important thing to look at if you are concerned about rough roads. Most TTs have Lippert frames, and the ones on some of the ultra-lites are flimsy and flex a lot. Some TTs have a BAL Ultraframe which is a good alternative. IIRC, Jayco Whitehawk has them, but I know Lance does for sure.
I'm not sure if Nash or Outdoors RV TTs come standard with shock absorbers or are an option, but they might be something to consider and look for. We had them installed this year and they sure help a lot, especially on roads with a lot of twists & turns and ups & downs.
If you don't know much about TTs, whatever you buy, I highly recommend that you take it to a good independent RV repair/maintenance shop and get a thorough inspection done, preferably before you buy too. With all the issues that TTs are known for, that's a long trip you are planning and you sure don't want to have a bunch of things to fix en route, especially anything that could leave you stranded a long way from a repair shop or mobile tech. I'd also make sure you have a good WDH along with sway control and have it all set up properly and tested before leaving.
Above all, make sure that there have not been any leaks in the roof and that it has been regularly inspected and re-caulked if necessary. A roof that has leaked can be the kiss of death in a TT.
If you don't know the history of a TT and the mileage on it, you may want to buy a set of new tires even if they *look* okay. You may also want to upgrade to one load range higher like LRC to LRD or LRD to LRE. Since you are considering a long, long trip, you may also want to install a set of quality tires that have a good reputation like Maxxis or Carlisle. Also read up on taking care of ST tires - for ex., do not exceed the speed rating and keep them inflated to the max. pressure shown on the sidewall. A TPMS is a recommended item.
I'd look for a brand that has a good reputation for support and service from the dealer or factory. The dealer for our first TT (bought new) was a disaster for warranty work. Rather inept (3 visits to fix the bathroom door!) and verrry sloooow.
Good luck! 🙂 I'm jealous of your planned long trip though and wish it were me... 😞