I visited in October. I did a full day in each park, and park to park on the third day. Here's what I did on my park to park day (note, did not do the same attraction all of these times in succession, I left and went back):
- Disaster
- Forbidden Journey five times
- MIB about 5 times
- Mummy several times
- Simpsons about 5 times
- Dragon Challenge
- Flight of the Hippogriff
- Jaws
- Ripsaw Falls
- Jurassic Park
- Hogwarts Frog Chorus performance
- lunch and snacks in the parks
- Hogwarts castle tour
- souvenir purchases
- and about 30 minutes of wandering around and taking photos in each park
I suspect there will be more crowds in May then the day I was there, but you should still have time to do quite a few things, especially if you arrive at opening and stay until closing. If you decide the lines are too long when you get there, then you can buy an Express pass. Don't buy it in advance.
Mummy, Forbidden Journey, MIB, and maybe Spiderman? have single rider lines. Several of the big coasters do too, but you said you wouldn't be riding those.