i am wondering if you are putting the cartridge in backwards.
one end of cartridge there is a little lip around the outside. (goes towards head) and the other end there is no lip and more likely more air space were the plunger on a spring goes into the cartridge.
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i don't like changing cartridges due to simple fact, they can be messy, more so if either end does not want to unscrew and getting a grip to get things unscrewed ((normally a rag / paper towel works.
and then once new cartridge is replaced trying to get the "plunger" end to screw in can be a pain. ((last thing that gets screwed back together))
it generally only takes a few pumps, and pressing the "air bleeder button" a couple times to get grease to flow.
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fuel funnels, oil funnels, grease gun share a common plastic container. and is located on shelf were all the fuel cans, various oils, and various spray cans for automotive / tractor are kept. for quick easy access.
normally there is a roll of paper towels stored right next to the plastic container, so i can take a piece of paper towel to wipe a funnel out or, have a couple on hand when a grease stuff.