whats swaying?? the arrows??
how bad are your fletchings wrinkled??? ive had some pretty bad...heck ive had some half falling off and some missing and they arrows still shot true...
my guess would be if the arrows are doin the swaying would be a tune issue from switching rests...did you tune after you put the new rest on?? once the rest timing is correct, you gotta tune it to get it shooting well again...