When I bought my first Morgan from Allon White I asked Phil Benning for tips on what and how to do things. His tip for greasing was to use a lever to pry up the damper blade plate and watch for grease exiting. This was before it appeared on gomog. I have a pneumatic grease gun so it is easier to manage with a simple trigger press than a lever version. A push action gun should be ok as well. I use a pry bar to raise the plate. It only needs a small gap.
Gomog is a good reference for many things and add to that the tips here in TM mean you will be ok.