Another long distance group to consider is the FarRiders (www.farriders.com)
Based in Australia and headed by Davo Jones, there are "ride to eat" days where we FarRiders cover a minimum 1000km in the 24 hours over any route you choose. The May 09 rides involved a combined total of about 125,000km during the 24 hours without an accident, major breakdown, nor traffic infringement notice.
Although 1000km days have been completed recently on postie bikes, your GT seems a great choice for such trips.
During the last 2 years I have completed 1000km days on:
Suzuki GSX-R750 (overnight 1000km, a 1500km day, 3000km in 60 hours),
BMW K1200R (1000km 3 times, 10000km in the first 10 weeks),
Blackbird (1000km on the first day),
Hayabusa (3500km in the first 5 days, 1000km in 14 hours over the Snowys including hitting a roo and getting a flat tyre replaced),
Kawasaki GTR 1400 (4500km in 5 days of twisties in the USA)
and even a Kawasaki ER-6F I bought on ebay from Melbourne and rode home the first day.
ps even did a 1000km on my MT-01 with its 1700cc engine and silly 15 litre tank