Both the Badger and the Norco are great tools for my purpose. I ordered both and they came in the other day. I finally got around to using them. The badger stirs without frothing unless you raise it up close to the top of the bottle where it can draw air into the mix. Get too close to the top and it will turn the entire bottle into a milkshake that's entirely froth. It takes about 30 minutes for all the bubbles to rise and break, then you're back to a totally clear bottle of juice.
The Norco straight attachment expands as it spins and does a great job, also. It will also create dense froth if you raise it up high enough to create a whirlpool at the top.
Cheap as they are, they are both good tools that I liked really well after the first test. I may have found my new favorite tools for complete and rapid mixing. It certainly beats shaking. I'm using these in 60ml glass Boston Rounds bottles filled with 50ml of juice.
Thanks to Fozzy71 for telling us about those.