How to animate two or more unrelated properties on a sprite GameObject using animation layers?

Question

I have a sprite in Unity 2019.3. It is animated like so (with provided mockups):

• Its base animation is just one frame; i.e. it has the same Sprite whether idle or moving.
• When the player is invincible, the ship flashes in and out. This is implemented by setting the alpha to 0 and 1 and back.
• The player can acquire up to three levels of shields. The is implemented as a child GameObject with its own Sprite (but not its own Animator).
• When a player acquires a power-up, they briefly flash colors. This can happen while they're shielded, invincible, or both. This is implemented with a custom palette-swap shader, not by replacing the Sprite.

These animations are all independent of one another, and can all occur at any time. For example, when a shielded player takes a hit their shield downgrades but they also gain brief invincibility. It would look like this:

A single state machine to account for these possibilities (and others, depending on whether or not I add other power-ups or mechanics) would be prohibitively complex. So I'm going with animation layers.

I was hoping that it would be as simple as adding separate animation layers with their own state machines, then marking each layer as additive. Nope. I have no idea what I'm doing.

How can I use Mecanim to animate my sprite as I have previously described?