a12vman wrote:
I didn't follow. My total run is ~ 22 Feet. I only have ~ 6" of fall to
work with over the 22 Feet. With only 6 inches, I would hardly have any
fall. Am I missing something here?

As far as the vent goes, can I get away with adding an Air Admittance Valve?
I don't have a vent stack anywhere nearby.

SNIP

6" of fall over 22 ft gives roughly 1/4" per foot, which is
acceptable.

http://www.codecheck.com/pg13_14plumbing.html
Fig. P5 shows slope for one application.

Fig. P6 shows install of air admittance valve
in relation to trap. Whether you can "get away" with it
depends entirely on your local inspector.

Fig P7 Combo vent does not apply to your situation.

Jim