comment on the Side-by-Side versus Tandem seating
QWI here, so not as directly relevant from an instructional point-of-view...
As a student, moving from the JP to the Hawk was a revelation and, like you, I loved the tandem set-up; it set you free. That said, a lot of my dislike of the JP depended upon whom I was flying with - the difference between the ex-Shack/V-force co-pilots and ex-FJ guys was very noticeable in my time. It wasn't their fault - with hindsight it became clear that they had not had that much stick-time themselves, regardless of instructional ability.
Then, Hawk TWU back to Lightning Training Flight. This could reasonably be described as hilarious (both bad and good), especially since on my course the 2-seater undercarriage collapsed on landing after the conversion phase and we did the rest of the course chased in the single-seater - which was wonderful. Then the engineers fixed all the Tubs just in time for the end of the course - literally the last 3 or 4 sorties - and that turned into a deeply miserable time! As we used to say, the best use of the T5 would have been to crash it into the simulator...then everyone would have been happy.
The T5 was a real dog's breakfast what with the reversed controls in the right-hand seat (albeit very funny when watching someone else tanking) and the fact that, if you were flying with anyone normal-sized, you had to get out of each other's way to move the stick. Check-rides were obviously stilted with blokes trying to pretend they weren't watching you when, of course, they were glued to your every move. Can't say I liked it, but it did make for a great experience for the passengers.
I instructed (tandem) both two-seat and single-seat at the sqn and OCU-level as a QWI and IP and would say that it made for a much better student experience for all the reasons described. In the USMC, we also taught an awful lot of the course (both WSOs and pilots and both 2-seat and single-seat courses) from the other jet, which was even better. I preferred to allow the 2-seat students - and, as a flt cdr, the junior front-line crews - to fly together, since they learned much more from the experience and did not suffer the decision-making gradient inevitable when a more experienced mate is in the jet. Not all the then-sqn cdrs agreed, but that was more a reflection of their risk aversion than the students'/crews' performance.
At the level I instructed, I never felt the need to watch the student's each and every move from beside or behind him. Indeed, from the comms discipline, formation-keeping, lookout and fuel calls you could tell exactly where he was looking, where his hands were and even what he was thinking without being in the same jet.