Will either Stability Acro or Coaxial allow me to engage it while flying normally (skids down) and then flip the heli inverted via aggressive cyclic input on the radio, then basically go "thumbs off" the cyclic with the goal of staying inverted and practicing hovering.

The manual explanations make it sound like I MUST activate these modes when already basically inverted. Is this the case?

Stabilization (Acro) – stabilization mode - inverted or upright, whichever is closer
at the time of activation. This mode is used for learning the basics of acrobatic
maneuvers. If the sticks are in the center, the model has tendency for returning
to the horizontal position.

Coaxial – stabilization mode - inverted or upright, whichever is closer at the
time of activation. The steering behavior is very similar to a coaxial helicopters.
Great for learning a hovering practices

Only Stabilization ACRO allows you to flip inverted.

All other must must be switched off, go inverted manually and then switch on.

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Goblin 700C Red Carbon, Cool Kosmik 200, Pyro 800-48, MKS X8 HBL 850/880 HV, Spirit-Pro, Jlog2.6GW, GPS-Logger 2
Jeti DS-16 Red Carbon+REX7

Thanks for the clarification