Lower kitchen sink drain pipe
Lower everything 4", that is your best option.

If that doesn't fit, then find a shorter air admittance valve and or lower the existing one as much as possible.

If that still doesn't fit, then cap the air admittance valve. Add a Tee fitting below where the sink drain connects to the vertical drain pipe. Connect a 90 degree fitting to the Tee to make a vertical pipe, then attach the air admittance valve to the top of that. You'll have a wet vent for about 6-12", but it should work correctly.