Keeping water level up to the pump and/or eliminating air up there:

I don't think there can be a problem with air in the rads or pump housing if
the system is filled from the bottom - from a hose going down from the
bottom of a "header" tank (pressurized expansion tank) that is at or above
the level of the top of the pump.
    - The liquid will go in the bottom of the entire system and force air
upward as liquid level rises 'from bottom', and assumng that there is a
bleed plug at highest spot in engine or pump (removed) or a peck cock valve
(opened) during filling.  (ideal would be to have a permanent bleed line
from that high spot into an 'always-partially-filled header tank that always
keeps the entire system full of liquid - air has to be expelled.
    -  Given, there may be air traps somewhere in the system, but the liquid
will either bypass them - or purge them as it keeps rising until it comes
out the "high point" (bleed plug hole or pet cock or bleed line connected
there and going into the header/expansion tank).

If you don't have such a header tank, then there should be a way to plumb in
a "fill hose" that is fitted to the bottom of the system (such as a pet cock
with an appendage for putting on a piece of rubber tubing), with "fill hose"
running up to be held above engine with funnel in it - or put top end of
fill hose on bottom of a siphon hose to siphon or pump out of your coutainer
of coolant.
    -  Fill the system until liquid comes out top of system.  Close petcock
at bottom of system.  Remove fill hose and put it and your funnel and/or
siphon, or whatever away and then start engine runs to purge any remaining
air and keep topping off the liquid level as air is expelled.

Does this make sense?  I'm talking about NOT having what I consider the
ideal system (pressurized expansion tank with fill line going to lowest spot
in system and with air vents from highest point in system into expansion
tank below liquid level).  I'm only suggesting that whatever OTHER system
you have, permanently install a fitting (valve or pet cock) at bottom so you
can temporarily install a removable fill line and, holding the top end of
the fill line above the engine & pump, pour in coolant so it goes in at the
bottom until it comes out the high point.

David Carter