There is no harm in draining out antifreeze once you've filled the piping with it (and hence removed the water). Air does not freeze and burst pipes.
You would need a lot less antifreeze if you hooked up a suction line to the pump (with a couple of valves or even just manually moving a hose) rather than dumping a bunch in the fresh water tank to pump out and through the plumbing system. A water heater bypass would save even more antifreeze usage, but if there isn't room to install bypass valves then there isn't room.
I simply blow out my system using a compressor. I realize there are (sometimes strong) differences of opinion on this, but so far it's been perfectly effective for me, in cold New England winters, and only requires about 1/2 gallon antifreeze for the drain traps each time. I do check for leaks using air in the spring before filling up with water. (This is particularly easy to do in my case because the check valve on the water inlet squeaks when even a tiny bit of air is flowing through it.)
