Thanks, Eric, for the gist! To help future searchers for on this topic, I found
this Kivy documentation on the CheckBox to be a bit misleading as it says the "active" (bool) describes which is checked, and claims that a
group of CheckBoxes causes the same behavior as a ToggleButton (ie takes on Radio button behavior where only one can be checked or pressed at a time). As it turns out, the
Behaviors documentation is the correct place to look, specifically the ButtonBehavior section. As the CheckBox had the "active" property, the Button has a "state" property (string) which can be either "normal" (unpressed) or "down" (pressed).
Note that even though ToggleButtons behave to the user by only letting one be down at a time, using the Python properties to change their states allows you to have several down at once. In other words, setting a ToggleButton state to "down" does not set all its siblings to "normal" - one must do that explicitly.