bouncing tenors I agree with Simon that it is a common practice on big bells and that by trying to "outlaw it" your tower captain is, most likely unintentionally, reducing inclusivity.
The stay on a 37cwt bell will be a chunky piece of wood. When set a bell of that weight will only be a few degrees of rotation (2°-4° I would guess) beyond the balance point. If you think about it the maximum energy that can be dissipated into the stay is the energy from the bell falling under its own weight from the balance point to the set point, so falling a couple of degrees. The ringer can only put energy into the system by lifting the bell from the set point up towards the balance. if the ringer exceeds the energy requirement to get between the set point and the balance then the bells comes off the balance and its mission accomplished.
Its a completely different scenario to say a learner ringing a lighter bell without sufficient control where they can pull hard at one stroke and bounce the bell off the stay at the next stroke hard enough to bounce off the stay and back over the balance at speed.
The stay is made of ash which is a flexible wood which is designed to absorb a certain level of energy without damage, exactly the same as a sledgehammer or pick axe handle does. Those can be used virtually indefinitely without damaging the wooden handle. I'm sure you know this already but it might help to be able to frame it in these terms with your tower captain.
In terms of techniques other than bouncing the bell off, I will try and describe what I do (as a 6ft, approx. 80 kg person). I go up on my tiptoes and hold the sally as high as I can with my arms fully straight. I then sink down on my toes and hang on my arms, this shouldn't require your arm muscles to be tensed, you are hanging rather than pulling. I do this to take the stretch out of the rope, the bell has not moved off the stay yet. Its hard to estimate what is required to do this, but I'd say you want to put 30-40kg on the rope, so about half my bodyweight. After the treble ringer has said "Look to", I start to pull the bell off. To do this I think about dropping down off my toes to being flat footed, ultimately transferring all of my body weight onto the rope, and if need be I start to pull with my arm muscles, thinking about lifting myself off the box, this brings the bell up to, and over the balance.
I think the key is that I treat the pull-off as one single movement after the step to take the stretch out of the rope. I'm never aiming to get it to the balance and then holding it there. I'd say that the whole movement takes something like two seconds. I think something to avoid, and this might be where you are hurting yourself, is trying to jerk the bell with short impulses of force. Give it one firm, long duration pull and believe it is going to come off the balance. If you can, try and practice it by yourself where you don't have the added complication of trying to pull off in time with everyone else.
The final point I would make is that it is not easy, people who are very good at it make it look easy. It takes time and practice to perfect it. I've turned in 2 ton+ bells to peals and I've still failed to manage to pull a tenor off and come crashing into the following change.