Growing need around the world? How many US states have banned lead ammunition?
My RFD has these on the shelf
Norma ECO Speed-22, he couldn't get them inside 6" at 25 yards in various guns, that is with a 24 grain bullet so a 1:16 should stabilise it.
Rebarrelling 0.22s

£800+ for many guns worth £<150.00!!
Subsonic 0.223, again

, you are going to need a heavy, heavy bullet say 70-90 gr, in lead free at subsonic speeds!! Firstly, .22 cast bullets are used for subsonic as they can be lubricated, copper bullets with that bearing surface may jam in the barrel; secondly twist rate is only half of the stability equation, speed is the other half so you are going to be needing a 1:5 or so at a guess to stabilise long, lead free, 0.22 bullets (I loaded 120 gr subsonics in the 25-45 sharps, 1:10 twist, they literally went through the target sideways, quiet though!); Finally, cost!! speciality 0.223 ammunition is going to be over £1.00 per round, £2.00 the way things are going, who is going to use that for volume rabbit control! Oh, and they will deform less, bounce more, carry more energy down range further as they will not slow as quickly as a deformed lead bullet. All in all a cracking idea!!
The market isn't crying out for a lead free rimfire ammunition because the vast majority of the world is still quite happy to use lead ammunition and will continue to do so.
Your sand trap is exposed to wildlife and therefore could be a risk, you may not be allowed to use it for lead in 2 years time . . . .
You clearly don't live in the real world.