we have this problem all the time,most europeans can fly in and leave usa by yacht on a reciprical tourist visa,but if entering again by yacht would need a full b1b2 visa.
as arriving by non commercial
but would think dept of home land security
can give you a better answer,helpful as long as you follow the rules.
also cant see why you should have a problem for a green card holder.
out side usa juristriction you all need to check in and out irrespective of nationality.
though it helps not to have a third world passport.............may find a canadian can actually go to more places without a visa than you can on a us passport.