1969 Dodge Dart issue with installing axles after thrust block removal.

So if the grease is not smashed flat, you're saying that there is enough clearance to not worry about removing the buttons in the carrier?
Buttons in the carrier, as in the "plates style clutch" this I do not know, you would have to try it. I have a cone clutch and it worked without removing the thrust block. The buttons would I am pretty sure can be removed using a magnet on a long stick.