Sounds like the check valve may not be holding unless under pressure. Or, the popoff weight is not being returned because of a weak spring and/or corrosion slowing down the weight to reset. Good luck you got this. Dave
The new check valves do need seated, some come with a dot on one side, to determin the best side to seat, and seating them is recommended, wood dowel light tap, to set. as long as the pump can draw air into the pump tube you should be fine.
If the issue is that the check valve has a minor leak and needs to be seated, you may be able to seat it by pumping the gun up briskly to high pressure (like 10 or 12 or even more pumps since it's teflon but don't overstress your pump arm) then open the pump arm and let the gun sit for a while so the high pressure in the valve pushes hard on the check valve and molds it in. It's not a guaranteed fix, but easy enough to try without tearing the gun down.
Are you sure that air is leaking out?At the top of the pump stroke the gun should be drawing air INTO the compression chamber.Perhaps the sound has you fooled?