These forum friends recommended I rinse the tub well, then just vacuum out the jets with a wet/dry shop vac. Mine is old and I didn't think it would be powerful enough, but I gave it a try as I didn't want to rinse with 400 gallons.
Lo and behold, I was able to suck a good 5 gallons out of the jets, I vacuumed out the rinse water from the bottom, and I was good to go. NO FOAMING ISSUES AT ALL!!!! Wahoo!
A forum friend also recommended putting the hose down the filter pipe thingy to try to flush out any "cleaning" stuff that remained. You could do both.
Hose first to flush the pipes, then vacuum out the jets.