On almost all players I've worked on, the holes that the pushrods go
through are bushed with felt.  This give an area equal to the thickness
of the chamber wall to stop air from entering.  I often lubricate them
like you did with Vaseline or some other thick lube.

Occasionally I have seen a punching of cloth used, as you suggest.  The
drawbacks, as I see it, are that there is very little area to stop air
from coming in: just the thickness of the punching.  The punching,
being on the outside, is more exposed to ambient air and will break
down sooner.  If the rod is not absolutely straight, or if it is pitted
or worn, or does not go back and forth absolutely straight, the hole in
the punching will wear large quickly.  A bushing with lube will be more
forgiving.

If I were you, I would bite the bullet and do a good job rebushing
those holes.  The rebuild will be tighter and last longer.

Jeff Davis, Seattle
Home of el Nino sun