How do I change inverter coolant fluid 'without bleeding' the system?

No bleeding just drain n fill let run till pump stops sounding like air . Then level the jug n go.

 

From the Repair Manual, engine and inverter coolant change instructions attached.

Also, per your other thread, transaxle fluid "inspection" attached. No mention of changing the fluid, but has some helpful pics and bolt torque spec, at least for the fill bolt. FWIW, the drain bolt on 3rd gen is 29 ft/lb. For some general tips, see also the transaxle fluid change link in my signature (on a phone turn it landscape to see signatures).

 

I did this

 

Preceding post is for burping the engine coolant, not the inverter coolant.

For the inverter:

Fill reservoir to mark.
Attach a clear plastic tube to the bleed valve for that loop and place the other end in the open reservoir.
Open the valve.
Turn on the car.
Fluid with bubbles will move through the tube.
When there are no more bubbles close the valve.
Turn off the car.
Remove the tube and close the reservoir.

Note, clean up any drips around the bleed valve thoroughly. Otherwise it might look like it was leaking there after the coolant dries up and crystals form.

 

Sorry, @pasadena_commut is right.