With a 6-speed, I doubt you'll notice a significant difference in the hills at speed unless you have speeds where you feel you can't find the right gear to get it in the rpm's where it is making good power. Your biggest improvement will be from a stop up until you get the rpm's up where it is making good power in first gear, that should be fairly noticeable.
I think finding one to do a test tow is a great idea if you can make it happen. Hopefully you can find one and be able to test it in a location where you can try it out in conditions where you currently aren't happy. $2500 is a lot of money, but worth it if it makes you happy. I'd hate to spend that much money and still not be happy. If that happens you might just want to temper your expectations.
