You don't have to blow out the lines. It just removes more water then simply draining with the low points, thus reducing any dilution of the pink stuff. Your method will work, it just takes a lot more anti freeze, because you have to get enough into the holding tank to reach the pickup AND be concentrated enough to work. There is almost always "some" water in the holding tank, even after draining. The simplest method of winterizing is to:
Drain the FW holding tank
Drain and bypass the water heater
Set the water pump valve to winterization position
Stick hose in gallon jug
Turn on pump
Open taps one at a time until pink comes out
Don't forget the outside shower if equipped, or the toilet
Pour 1-2 cups of anti freeze into all the drains, and in the toilet bowl
Have beer (optional, wine, bourbon, kool aid)
The whole procedure will use about a gallon or a little more.