When the plumbers filled my system (this was awhile ago, things got rearranged and no longer have a need for antifreeze), they put a hose on the suction side of the pump (they had installed a drain valve there), and just stuck that hose into a bottle of the antifreeze and opened the valve with the pump on...it sucked it right in. Shut it off as the bottle emptied, put a new bottle in place, open the valve until done. If you'd drained enough of the system to make room for the antifreeze, you wouldn't be throwing it away.
I only saw this once, and may have missed an important step, but that's the basics of what I saw.
Hopefully, somebody that does this on a regular basis can provide more detailed steps.