Thanks to everyone who responded. I had a big long response composed, then my browser decided to dump it. So I'll summarize.....
Tramlining is the tendency for tires to follow grooves, ridges, or other features in the road.
Now I have more research to do. The TrueContacts (all 3 of them, Tour * 2 speeds, and non-Tour) and the Cooper CS5 (both of them, Ultra and Grand) look like front runners.
I didn't even know Hankook made tires in the USA. I'll take a look at that 737, too. (Hmm... no 737 or H737 on tirerack, but their reviewers are not kind to the Kinergy GT). Can't find much in H737 reviews elsewhere.
Heck, I'll look at all the tires mentioned here. Almost all. I want the option of not using the winter tires, especially as they are getting worn and the budget is tight, so I do want to stick with All Seasons. I'll pay for quality, but just not for a name.
I figure I can buy now on closeout, or in 3 months with a rebate. I'll post what/when I get. Until then I'll review any more recommendations.