I would, because I do it. Granted my bike is a little lighter, 385lbs, but the concept of what I do is something that will work just fine for you. You use ratchet straps to secure it to the Camper jacks and carry some of the weight, not all, just some, and make it super-stable. I've done it many times, no damage what so ever.
And I'm sure a lot of people will say I'm crazy. But I've done it many times, I'd ask from the people who are about to flame me and say no, to show why rather than just speculate. (putting on flame suit now).
My camper weighs over 6500lbs, that's over 1500lbs per corner. Asking that same corner to help hold up and stabilize your bike will be fine. It's a beefy frame under there.
In my case - the only drawback, I can't get the back slide all the way open, but I can get it open enough to get in for a bathroom break.
