Do you have a friend with a well equipped shop with an air grease gun?
I have an air-powered grease-gun and you would be amazed how many people come over just to 'bust loose' a plugged fitting. Only use the air gun to blast through the plug, though. It is too difficult to control for delicate greasing. Can blast right through the seals if you aren't careful, causing more problems than it cures.
If you can't think of anybody offhand with one, there are still a few things you can do. Wire brush around the zerk to clean everything up good, and check it over. Hopefully, it will be a screw-in and not a press-in zerk (the press in ones don't have wrench flats). I am betting it will be screw in. Unscrew it, and look at the underside of the zerk. Is it packed with gunk? If so, clean it out with an o-ring pick, or small drill bit held in your hand. Be careful not to damage the check ball mechanism. Put the zerk alone in the grease gun tip. Pump gently, ensuring grease will go through the tip. If it won't you need a new tip.
While you have the zerk off, take a pick or drill bit that loosely fits the hole, and clean out any junk in it.
8 times out of 10, once I clean out both the zerk, and the hole, I can now get grease through it with a hand gun. I still keep the air gun for extreme cases. Bought the thing because I just couldn't get grease in a fitting on a tractor, no matter what I did. The replacement parts were over $250, so I gambled the price of the gun, and it (barely) blasted through. Word of caution, do NOT use a hose on the air gun, use the steel pipe. The hose can burst, shooting grease through the skin.