Okay folks, I believe I have a handle on this... and a plan.
Tim over at microbe organics sells a machine that I believe makes kick ass tea, based on massive oxygenation.
Folks here make damn fine tea with air stones and decent, but not massive, oxygen levels.
So what is the purpose of compost tea, and later vermiculture tea?
It is to multiply the heck out the bacteria, microbes, nematodes, etc to inoculate your soil with more than you need of these helpful little buggers so your soil can be alive with critters that will fetch nutrients for your roots.
The "more than the soil needs" part is the key to the answer.
Both approaches are more than adequate, so I should choose the inexpensive and quiet option.
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The analogy that made it clear (to me) was my rain guage. My rain guage holds 5 inches of water.
If option 1 is two feet of snow, and option 2 is one foot of snow, it doesn't matter... they both fill the rain guage to overflowing
I will go the aquarium pump and air stones route, trying to get something large enough and maybe a tee or gang switch that will help me create a stirring, roiling or swirling motion so that the air bubbles spread around and fill up any low o2 backwaters that might breed anaerobic bacterium and flagelates and stuff.
Thanks so much for your valuable contributions to my decision.