Tex,
It is funny how some people seem to think that the LS650 is a bit of a toy. Many of my friends kinda laughed at my wife's bike (until they realized that they were NOT running away from her on their 1400cc machines). I think you will find that the bike will do that sort of trip with no trouble. You may not find it so easy, however - especially your backside.
The only long ride I ever did on an LS650 was to Leesburg, FL for their annual bikefest. I was riding with three other pals - all of whom were riding bigger machines. I had no trouble keeping up with them for the 90-minute ride but, by the time we got there, my butt was not happy and my feet were pretty numb. The bike was gleefully thumping away, however. The one saving grace will be that you have to stop every 140 miles or so (for fuel), so you will have plenty of break time!
Some other things to watch out for (taken from comments my wife has given me):
Interstate riding can be challenging on this lightweight machine. The wind and turbulence from larger vehicles can be brutal. Be careful how you load your bike - the extra wind load of your luggage will affect handling and aerodynamics. Are you planning to take the back roads?
My wife sometimes complains of a numbing vibration in the handlebars (on long rides at 60+ MPH). I am not sure how real this problem is - it may be that she is riding with a death grip on the throttle (or some other quirky thing). I didn't notice this on my Leesburg run, but I installed Kuryakyn iso-grips to try and help her. The jury is still out on those (I think they helped some).
The OEM footpegs really do cause numbness / discomfort in the feet - at least for wifey and me. I put on some cheap floorboards from JC Whitney and those made all the difference in the world. You may want to look into some alternate pegs before you set sail - some highway pegs, perhaps?
To help with the saddle issue, I put on a Harley-Davidson Sportster seat, which provided some relief (but not enough yet). I don't know what Sargent does to the OEM seat, so that may not be an issue for you.
After the modifications I mentioned here, my wife and I can now do our "beach runs" with no problem (230+ miles round trip). That's essentially one full tank of fuel each way - in one day. We usually only stop for fuel, and she can now ride the whole way in relative comfort - keeping in mind that this is not a touring bike. She still is not 100% happy with the seat, but I added some memory foam yesterday. We'll see how that works next week when we head for the surf
.
Good luck, and watch your back out there! If you're passing through this way, and you have time, feel free to look us up. You can PM me here if you wish.