I would work on my form before I put on a muzzle device. Unless I could have a suppressor, which you’ve already stated that you can’t. Consider it a training motivation/goal to find your best form with the least amount of muzzle jump. There will be some basic physics involved that will make it a challenge with that stock (the bore line is above the top of the butt of the stock), but it is certainly reasonable to expect minimum muzzle rise with a .243 with good shooting form and that rifle. Search on here for ‘practice’ threads, look at sniper’s hide, etc. You’ve got some limitations in that you can only shoot off a bench, but look at professional bench rest shooters and their setups. You’ll see minimal if any muzzle rise.
For starters I’d look at seat height vs bench height vs rest height. Often times the setup is too low and that forces a person to setup incorrectly and this magnifies the effect of a stock that isn’t built for recoil mitigation. A higher front (and rear if you’re using one) rest can help with this.
You didn’t say this exactly, but if after the shot the scope goes up and to one side then you have a ‘weak side’ and your form is not as solid as it could be. The physics says the force of recoil will go to the place of least resistance. In this case maybe something like a torso that isn’t set up square so the stock can squirt off to one side or another. Same type of thing with the muzzle rise. Figure out how to mitigate that and you’re off to a good start.