Getting a second flying sea tour is pretty easy for a hard-charger, and usually happens as a disassociated tour. Anybody on CAG-staff will still be able to fly, and squadron Super-JO's (typically) are guys who were selected for WTI out of their first sea-tour, then went to the WTU/Fallon/FRS for 3yrs of shore duty, and are coming back to the fleet to be the Training Officer in a squadron. These guys are LT's and probably LCDR Selects. They will select for DH directly out of that tour as well. It's a big commitment in the E2 community to go WTI... you're going to spend A LOT of time at sea, and way more time on the road than your peers when the squadron does happen to be on the beach. It's one of the primary roads to command, but you spend a lot of time away from your family. If you don't mind mainlining the kool-aid full strength straight to the jugular, then WTI might be for you.
Guys will get picked up to Test Pilot at the very end of their JO tour, or very early at their first Shore Tour depending on when the boards are and when they actually got to the fleet. There are also several ways to become Test Pilots, and there is a selection board at Millington. You must submit a package, endorsed by your CO and probably CAG and the Admiral. The package goes to the board and you compete agains a couple hundred other guys. If selected, there are a couple different ways to actually become a tester... AFIT, Direct Entry, etc... and after you graduate from TPS, you owe your payback tour as a tester at one of the VX's. Some guys have time after their test tour to have a mini-tour doing something prior to DH screen... especially if they don't screen for DH on their first look.
Unknown about how the AEDO job works, but I was under the impression that guys who were pilots and became AEDO's don't fly anymore.