This was something I was pondering yesterday, I was on a walk near an Iron Age Fort that also has a quarry nearby. (Industry and noise near history/preserved locations)
You can't hold back the tide, more people want to ride powered-bikes in the countryside.
For me the best solution is to have separate routes that keep the bikes to farmer's lanes and muddy tracks. Would it also not be great to say only electric bikes allowed so you reduce the noise pollution specifically?
It's a way to safely introduce electric bikes and gives the people what they want.
Anything else and you will continue to have lawless biker behaviour damaging more vulnerable spots.