How crazy is it to land at AMM and drive into Israel? It appears to be less than a two hour drive to Yerushalayim, and there is plenty of direct availability in J for 70K AA.
As long as you are not an Israeli citizen, then you can use the Allenby Bridge (King Hussein) - which is the closest to Yerushulayim. You would have to take a taxi to the King Hussein / Allenby bridge. (On the budget side, you can take Sariyah Airport Express from airport to Amman city). In Amman, there are frequent taxis that regularly leave from Tabarbour bus station everytime they fill up with 4-5 passengers and take you to the bridge/border. Once there, you go through the Jordanian border formalities and then you enter no man's land. From there, there is a bus for the 2km over the bridge that leaves when they fill up. Then on the Israeli side, there are two terminals, one for Palestinians and one for non-Palestinian. You have to give in your luggage, and go through the Israeli immigration formalities, and then it's 45km to Yerushulayim. There are vans leaving frequently going straight to Damascus Gate/ Sha'ar Schem / Bāb al-ʿĀmūd (in Arabic). The other two borders are near Beit Shean and the other near Eilat are very quick (no crowds), and do not have the hassle and the no man's land in between. Alternatively, fly with Royal Jordanian the short hop to TLV. Private cars cannot cross the Allenby/King Hussein bridge. The other two borders, private cars can cross, and they change license plates.