The R22 datcon works on engine running. The 44 runs on collective time.

That varies a bit. My machine R22 has both meters (as do many)
You are allowed to choose one or the other as your "metered Time" but you
can't change from one to the other. If you use standard Hobbs on the oil
pressure line use the numbers as they are shown. If you choose to use the
collective meter you have to multiply the time by 1.12 to get the time.

arbitrary time. If the school owns the aircraft I'm sure they want the
engine to go TBO and so treat it kindly.

Long runs at low engine RPMs have a propensity to foul up the plugs if the
temp is already down. Especially the lower ones. If the engine is hot then
its fair enough but after 5 mins I would have thought it was cooled enough.

a right yaw that was so extreme you had to add FULL left pedal to stop

Yep. try it in a howling crosswind. Had it so strong at times that full left
pedal wasn't enough. In that case - settle into the wind put it down. forget
about trying to line it up with the H. Come back later with the wheels and
turn it round.
He didn't say violent, just shimmying and shaking. A slow and high
approach

Maybe those cross winds again?