Ok, I see what you mean by having more fine control and using cycles. I've set up two different cycles tests (full body jump and simple legs move). I've tried various ways to implement them and don't seem to have them as a correct child in the file structure. The jump one has a new head/body/limbs so I need it over the Mouth, Head, & body layers. It works, but I'm not sure how to make everything else be invisible when it happens (as shown in video link below). The LegsMove Cycle also works, but doesn't replace the existing legs when it is on.
VIDEO example here:
With the desired subpuppet selected in the puppet panel (as shown above), apply a new Cycle Layers behavior using the "+" menu in the properties panel and choose the options you want.
To have the key trigger (W in this case) hide all of the sibling layers, add an exclamation mark after it in the layer name (e.g. "Frog Jump Cycle (W!)". Without the exclamation mark, the layer will be shown when the key is pressed, but all other layers will remain showing too. This is good for additive thing, like a lightbulb appearing over your head. The exclamation mark (exclusive mode) is good for swapping things. You can use grouping to limit which things get hidden.
See the doc on Cycle Layers for more details.