score:4
If you walk from Amman to Aqaba you'll stay quite a long time in Jordan.
I guess you'll see Wadi mujib, Petra, maybe even Wadi rum ... It could worth to buy a Jordan pass.
I don't see any problem to join Israel in your itinerary although you should check the border status few days before you arrive.
Upvote:6
From a visa point of view, your plan sounds fine. Be sure to arrive early at Ben Gurion, because you may get selected for extra questioning. Enjoy your trip!