Joe, it IS possible to leave your bike in Jordan and enter Israel via the King Hussein crossing without creating problems with the carnet. I got the idea from two Kiwi bikers that did it a month before me, and then I did it myself.
The reason it works is that the King Hussein crossing is sort of an unofficial crossing that allows Palestinians living in Jordan to visit the West Bank. The Jordanians will NOT give you an exit stamp in your passport, and they will not even look at your carnet. The rules are different there. The only problem is that you are not allowed to ride across the bridge with your bike... which is why you must leave it in Jordan.
Using this crossing, I managed to visit Israel and avoid the stamp - but it's not a sure thing. (Disclaimer!) When you get to Israel, they will probably tell you (like they told me) that their policies have changed and they stamp every passport now. But, if they like your story (travelling overland in the region with motorcycle, etc, etc) they may choose to keep your passport clean. If they don't like your story, they may just stamp it. It's a gamble.
Of course, you need to leave Israel before your Jordanian visa expires.
Oh, and one more thing... If you enter Israel using the King Hussein Bridge, the Israelies put a sticker on the back of your passport when you send your bags through security. When you remove the sticker, there remains a patch of glue where the sticker once was. It is very important that you remove the glue patch completely before trying to enter Syria. Some gaurds look for this sticky patch to see if you've been to Israel!