To be honest, the .243 is not (in my opinion anyway) going to help in any way here. Similar muzzle bark, slightly less recoil but completely different trajectory and it's another firearm to feed. Plenty of soldiers learnt to shoot going from nothing to .308, so it can be done. It's just a case of researching the techniques and if you can get to a range with someone that's experienced with hunting situational shooting that can coach you a little.
The point about the Peltor noise cancelling is that different to industrial PPE, they only shut off noise past a set threshold so for industrial purposes actually don't comply with H&S requirements. What the point of the exercise is, is to get away from the noise effects of the muzzle gas jetting (it's similar to a high pressure compressed air release and a similar level of potential damage). The suppressor tames the worst of the gas jet expansion noise by reducing the velocity of the gasses leaving the muzzle, but doesn't remove the supersonic crack from the projectile or the gas pressure wave which is the equivalent of the compressed air release.
In your position, you're doing the right things by thinking through and asking the questions but one of the issues with the internet is wading through the multitude of replies which are all correct in their way to find what suits your situation and objectives. My vote such as it is, is to stick with the .308 and make it work for you. Money saved makes for more ammo for practice, and once you've got confidence with that you won't look back. Noise from the gunshot is one major factor, suppressors help and cap it with whatever hearing protection you have on hand that suits and is convenient. If recoil force is still an issue, you can upgrade the recoil pad to a limbsaver or a pachmeyer version or add some weight into the stock which slows down the rearward boot...
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