I did this trip last spring. The overland routing will take you via bus across the Sinai directly to Nuweiba, where you catch a ferry to Aqaba. I took a taxi up to Amman from Aqaba, it wasn't too bad. Jordan is a relatively small country.

The problem is the Sinai bus ride is horrible, and you'll need an overnight ride to catch the ferry in Nuweiba. The ferry wasn't too bad; indeed it was pretty nice if you get the more expensive fast ferry (but still cheap). You don't need to be on a tour bus to get it, just make sure you're early enough to buy the tickets and insist on that ferry.

The problem was at immigration, or rather before immigration. They took all non-Jordanian and non-Egyptian passports and then left all the foreigners on the boat while they processed all of them. Finally, after a long wait, we got off and they gave us all our passports with the stamps already in them. Man, it took forever.

The entire trip via land/sea was way too long. I don't think I'll ever do it again. I know, the airfares are very expesive given the actual flight distance, but the saved hassle and time is very much worth it.