First, Congratulations! I'm so glad one of us grabbed that beauty. And that price!! One of my all time favorites! If I didn't already have one, I'd have pounced on it!
Second, LMB absolutely can strengthen the handles. I don't know if they can get them back to their original color without using dye, but I have had handles that made me nervous, re-tubed on at least one bag. It was an 04 WE that had been carrying too much weight before I got it. The entire tubing can be replaced with a slightly longer one, which will reinforce the handles all the way to the base of the handles, so they are again firm at the rivet. I believe there is another option, and that is to add something to the existing tubing that will firm up the base but leave the original tubing alone..
Best to contact them to get information as to best way to go, as well as pricing. I don't remember what it cost, but I don't think it was prohibitive. Good luck!