I've tried most of them
It looks like I am in the same boat as Max. I also own a GS that I will never get rid of and I too wanted another ride that was more relaxed. I agree that the Sportster won't fit the bill because of it's riding position. I tried the big Harleys along with the Victory's and big Triumphs and found the Triumph has the best fit of all.
If you like Harley cruisers you will love the Triumph Thunderbird. Get the 1700 as it has more power and it feels great at any speed, and the sound is really something to listen too.
I also have to agree with Mrmerlin about his comment on the Triumph Rocket. I was all ready to get a Thunderbird Storm until I got a chance to ride a Rocket Roadster. For bigs guys it's has a near perfect riding position and the power.........well it's exhilarating. Surprisingly easy to control once you get used to the torque but it can be addicting. Try them both if you can.