Even where there are "no codes" for building, there ARE codes for human waste disposal. Your health department regulates septic systems and will permit them only after the proper testing is done. This is a public health issue.

So, I suspect that you really want to avoid going through the roof with a vent so as not to tip off your neighbors and county officials that you've put in an illegal septic system. Any "plumber" who suggests an AAV for the whole bathroom venting is NOT a plumber and should not be allowed to touch your pipes. What you have may not be under local building codes, but your state does follow some national building codes and you would be wise to contruct anything according to their guidelines. IF you want any type of insurance or resale ability at a later time that is.

An AAV is not designed to ever be the sole or only vent in a building.

It is only designed to be a supplementary vent when there is at least 1 vent to fresh air.

You should therefore never use an AAV in this situation because it will actually cause problems with venting if you do.

Instead run a standard vent through a side wall or gable end if you don't want to run it through the metal roof.