Maybe I'm not reading this right but if the cap is going on partly then popping off, I don't think you have the incorrect size.
there's too much difference from one size to another ie. 1.78", 1.98", 2.00", 2.33". OK the 1.98 and the 2.00 are fairly close. I think that it might be the way that you're trying to put it on. If you held the cap centered to the hub and tapped lightly all around until it completly seated...tap through the piece of wood if you must. If worse comes to worst, they're only about $3 a pair. Go out and buy the two closest sizes to what you need.