Sorry, I don't have the link of the original thread right now, but if you have a look at my posts, you should find easily (it's on the first page of the middle east section).
What happened was that Jordan customs and authorities are scared to death that someone could do something in Israël because of a negligence on their side. So they're extra careful. This extra carefulness was acted by my entry refusal: they were convinced that I would have been turned out on the israeli side, and therefore that they would have been blamed for letting me in in the first place. Now, if the same guys are still working at this border (rather nice people), if you say that some other motorcyclists have crossed the border already (one of them with a french registered blue and white BMW k100), I suppose it should be no problem. Cars get in easily...
As regard to the document I got in Amman, I really don't know what it was: I got sent from buildings to buildings for a while, until I kind of lost patience and ask them to write me any bloody document that would get me through the first gate (my girlfriend was landing few days later to join me for two weeks. Knowing I was in Syria at the time, she got the interesting idea to include Tel-Aviv in "any city in the states surrounding Syria"...). I got the document, and it work. I still don't know what was written on it.
The vehicle stamp on the passport is a different issue. It can be either in English, OR in Hebrew. In the latter case, it is a complete give away. In the former, it depends on the guy at the Syrian border.
I had a single entry visa for Jordan, and got a new one when I came back from Israel (a double entry visa is a give away too...). You therefore have to pay twice the visa, the exit tax and the compulsory insurance. You can get visa at any Jordanian border, as far as I know.
For Israel, bring your green card: insurance is compulsory, and cost about 100$ at the border if you don't already have one.
Hope this is clear enough, and if you have any questions, don't hesitate.