Yes, you are right Matt, it is much less messy when you drain the block first and take the lower hose off of the water pump.

I looked at that connection several times, as I've dumped coolant from the upper end of the lower hose in a much more controlled fashion, once the block drain finishes. I use a vinyl hose snaked behind the left front tire to drain the block--hastened by pressurizing with a garden sprayer plumbed to an old expansion tank pressure relief cap, but I decided not to go that route just to change the radiator, with the worsening weather and the hassle of burping the head afterwards.

Another technique I've tried is taking a knife to the lower hose in the middle area where it is open to below. This hose was fairly new, and honestly the knife method (cut bottom half section and bend hose downward) isn't that slick either.