Two things I noticed missing in this thread is THE DRAIN LINES. and the EXTERNAL WATER LINE direct to the sink. I take care of them this way: I open the drain line removing as much water as possible,(blowing?) and then I run antifreeze through the faucet and down the drain until I see pink at the outlet..Then I rotate the faucet to the up position before stopping.Then I open the external water supply and reaching in, push the anti reverse flow valve so as much water as possible drains out. Then I open the external water supply valve on the faucet and some pink should show at the inlet. If not, I fill the faucet again and repeat the process.
Now you have ALL your water lines antfreezed.
Note, if you have a toilet, and or another sink in the head, you may have to devise more methods to treat all those lines, including the holding tank(s).