I did the Round the Med trip in 2002: ferry boat Genoa – Tunis, then Libya, Egypt, Jordan, Syria, Turkey, Greece and back to Italy

As Italians we needed the visa in advance only for Libya and Syria. The other visa were issued at the borders.

It’s likely the Libyans pretend you to have an escort (guide + policeman) for the all time you are in the country, of course at your cost. It was not mandatory for small groups in 2002 (we were in two on one motorbike), it became mandatory for everybody later, now it’s quite uncertain, especially if you travel only along the coast. But it’s something that you should find out before asking for the visa.

The border Libya – Egypt it’s very slow and painful, it took almost the full day.

The carnet is needed in Egypt, highly recommendable in Libya and convenient in Syria. The cost itself of a carnet is few hundreds euros or less. Then you need the deposit related to the value of the bike, but you don’t need to have that amount in cash. A bank, or an insurance, guarantee is fine, and you pay just a small fraction of that amount as a fee to the bank or the insurance (of course, as long as you exit your bike from the country which requires the carnet).

Finally, to get from Egypt to Jordan it’s recommendable to take the ferry boat Nuweiba – Aqaba. In this way you avoid to cross Israel: indeed neither the Libyans nor the Syrians allow you to enter their country if you have an Israeli stamp on your passport. To ask the Israelis to stamp their visa on a separate paper (they will do it) it’s useless, since you will have anyway the exit visa from Egypt in you passport.