I have never heard of this halacha. Very interesting. I’m a woman so i guess it doesn’t count for me, but i can only fall asleep on my back.
As for these actions being part of your kiruv, if i were that kid, i too would be turned off. Even a non- BT teenager probably would be. And if you know this is a shabbaton of BT boys, going around and ” inspecting” to make sure they arent being mechalel shabbos in private…#1 they probably lost all respect for you if they had any to begin with, #2 treating them like little children who need to be checked on and controlled probably made them want to be mechalel shabbos even more.