I use a Milwaukee cordless grease gun with a flexible rubber hose, it makes sneaking in those tight areas bearable. The tip is a type that has small teeth so it grips but doesn't damage the zerk. I know Ryobi has a similar product.

Amazon has boxes of zerks for cheap. I've changed out many of mine for the ones with better angles. On the older machines I think the manufacturers just put what zerks they had on whether or not it was what the application needed.