Finally, by running the pump with the dump valve open for
a short while you'll remove the majority of your air.

Larry,

 

Au contraire, mon ami.  The only circulation is in the lines running from the pump to the dump valve and back to the pump reservoir.  There is no circulation thru any of the actuators.  Thus, while this is a useful procedure, unless all the air is in those lines it only clears them.

 

It is useful, whilst on jacks, to alternate several times between powering the gear up/down and then running the pump with the dump valve open to rid those lines of whatever air was picked up from flow to and fro the actuators.

 

Grayhawk