Andi, I'd be blaming the freeze/thaw and poor drainage situation much more than the roses for your problems. Zone 6 is not terribly cold for most roses. My aunt and grandmother grew famous roses in Regina, Saskatchewan for years. I think it is zone 4, but it may be 3. But no rose is going to thrive in poor drainage, and unprotected from freezing and thawing. When you move, get a truckload of compost to build up (up!!) a nice bed before you plant your roses again. They will do great, no matter what kind they are. Don't know about where you live, but here, compost is free from the local landfill and it's excellent.
Rose breeders graft onto more robust rootstocks to make their grafted hybrids stronger and more disease resistant. I can't imagine that very many own-root roses would be better than some of the HT's I grew. The breeders also graft onto rootstocks that bloom more often than the own-root roses. Used to be a bloom cycle every 6 weeks was good, but now we have types that bloom almost constantly.
In Florida now, but I lived up the road from Paul in Salt Lake City for 20 years and grew fabulous HT roses with no great amount of sweat or maintenance. I did fertilize them in spring, keep them well watered through summer, and prune them in late winter, but that's about all. We had terrible clay soil there, too. I amended the bed before planting with a whole bunch of compost, and top dressed the bed a few times over the 20 years, I'm guessing.
Let's see, I had Tropicana, a couple of Double Delights, French Lace (maybe that's a floribunda?), Brandy, John F. Kennedy, a gorgeous red that was bred from Chrysler Imperial but I've forgotten the name, Peace, Pascali and a really great yellow one, again forgot the name. Plus a bunch of floribundas, a climber and Queen Elizabeth grandiflora that was 12ft. tall and wide. They all would start out about 2ft. in spring, and by fall would be 5 to 6ft. tall and 4ft. or more wide. I'd often get 4 bloom cycles in a season, unless there was a cold spring or a very early fall frost. One fall I had roses blooming in December!
