What time of year is your trip? I don't know what your timeline is for getting to the Dead Sea on Day 3, but here's one thing to just think about or look into...

The second time I visited Jordan, we only had one night at the Dead Sea. We were told that the beach was open until "sunset." This was in the winter, so perhaps sunset is earlier, but we had a late lunch after check-in and then got to the beach in late afternoon. To me, it was certainly not sunset yet...it was late afternoon but the sun was still shining. We were told we couldn't swim (well, float) in the Dead Sea because the beach was closed for the night!! The beach didn't open until 9 or 10 the next morning, but we were leaving the hotel by 9, so we couldn't swim the next day. We had to beg...almost in tears....before the lifeguards said we could get in the water, but only for a couple minutes and only right at the edge. It wasn't that enjoyable with people breathing down your neck to hurry up.

If you were wanting to get in the Dead Sea, I would maybe ask your hotel about their beach policies for the time of year you'll be there so you can make sure to get there in time after your hike. It could be a huge disappointment not to even be allowed into the Dead Sea!!