Ok, watched the vids and heres a couple of points...
That yard is super rutted. Just because a machine can travel/mow at X speed doesnt mean you can do it at that speed. You have to work to the conditions!
Dont ever sit with your back up against the seat back unless its super smooth. The rocking motion of the machine gets transferred into the body. Commonly know as "back slap." I miss the flex seat for precisely that problem!
The part of the vid with your miss's jumping out of the seat was a classic!
The hydros on the SZ are really strong and sensitive. Trying to get up to speed quickly, especially over ruts will for sure make the front end light and or jump. Looked like ( as your going over the ruts,) its making you push/pull the levers. Basically, you know where the rough spots are, slow down over those areas. I have one property in particular that I can go flat out but near the end of the run there is a deep rut caused by a ute. I know I need to slow down or Id get thrown out of the seat!
The deck bounce looks like a problem but I wonder if the springs have been tensioned off enough. Could even try taking them off completely but it will make the deck pretty damned heavy. That said, deck bounce is caused by rough ground and trying to go faster than you should. Youve gone from a much smaller, way less powerful and much slower machine onto arguably the most hard core machine out the. Theres going to be a learning curve! The wheel base of the SZ is different to what your used to and you need to take that into account. The wheels are going to find high/low spots you didnt feel before.
I agree that the deck can be light and bounce but Id rather have that than my knee getting screwed up more, caused by 2 previous model SZ's with cr@p leverage on a heavy deck.
How long have you been mowing that property? I bet if you mowed it on a 30 or 45 degree angle the ride would be sweet or at least MUCH better! Give it a try! You wouldnt be hitting those ruts square on and thats whats causing you most of the problem!
Im just trying to be straight up with you mate. At the end of the day, going off those vids, I dont think its the machine. I think you need to adjust your methods or fill the ruts. Like I said, just because the mower can go 15mph, doesnt mean you can mow at those speeds.