I looked into it and the idea seems like a good one. Jordan is safe to travel, as is Israel. My thought was that once I arrived in Cyprus I could get a ferry over to Israel, cycle over one border to Jordan for a little tour, then cross another border back to Israel. I looked into it and still haven't ruled it out.
From my own research, May seems like an ideal time to go, and your going on an organised tour so you have nothing to worry about and the routes will be navigable for all ages. I estimate I should be around about that time, so if you see a poor sole sweating buckets and looking a bit lost, all on his lonesome, stop and say hi, it might be me

but no, I can't see me being there at that time.
I asked my daughters if they wanted to meet up with my on route at some point to cycle a little way with me - at my expense of course

- but they just looked at me like I'd lost my mind. They are 24 and 22 (that's their ages not their names), so maybe they just love their party lifestyle too much. All the best.