There's no guarantee's that you'll have the same good luck with the 07 street glide but there also is no reason why you can't. I've ridden to Washington DC, Blue Ridge Parkway, Niagara Falls, Arkansas, Sturgis and California, twice.
The only time I had an issue that could have caused me to lose time on the road was the trip to D.C. when my bike's rear pulley bearing went bad. This happened on the first day of the trip and I was fortunate to come across a dealer who got me fixed up in a matter of about an hour and a half.
But.....that problem did NOT leave me stranded on the side of the road since I was able to still ride the bike when I got to the dealership. On my last trip to California my radio quit working after a rain storm in Kansas. This, of course, did not effect the running of the bike but a dealer in Temecula, CA was able to get it working again by pulling and reinstalling the fuse. Sort of like rebooting a computer I guess.
The good thing about riding a Harley is you usually are not too far away from a dealer while traveling in the US. When riding long distances, I try to stay in a town with a Harley dealer close by just in case I need to have any service done. You just never know if you need a part or two. I needed a spot light when I was traveling through Arizona the last time when a rock shattered it.
As long as the person who has owned that Street Glide took good care of it and you continue the same you can expect good reliability compared to your EVO. I doubt you'll feel like you made a mistake getting the 07. Good Luck!