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Hi, I believe you are on the right track as most backfire issues are due to a lean condition.
Is the check engine light on? If it is get a scanner or a code checker from your local auto parts store and see what the codes are.
If no check engine light then doing a compresson check would be smart just to verify the mechanical side of the motor. If you are able to do a cylender leak down test that would show more then the compression test as far as the mechanical soundness of the motor.
For a vacuume leak to cause a constant back firing issue (I assume its constant due to your remark of covering the valve body and it stops) it would need to be substantual almost to the point of you being able to hear the sucking sound. If you cant hear it then take a can of carb cleaner and spray around the vacuume lines and intake to find it. The engine should rev when the spray hits the leaking area.
Make sure the nuts and bolts for the intake to head are tights and see if you can see if any part of the gasket has been blown out or sucked in.
no cold air blowing out when ac is on but low pressure