You know, you could move the entire signing process onto the card, and I am doing that

You are forgetting that the average user can need to sign up to 5 events/sec. AUTH, media uploads, etc

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I'm not forgetting, I'm just ignorant!

Backlog and batch sign?

Doing signing on the card was the first place I looked. I found secp256k1 seemed poorly supported on yubi and other platforms. Maybe wrong.

Also, NFC cards are very cheap.

Thinking of ways to get 100's and 1,000's of users onboarded cheaply without them being able to stuff up and leak their keys.

Smartcards are also cheap

Also, batch signing does not make much sense.

You need to send the AUTH event immediately for example

Are you using javacards? I've actually implemented something similar to Rod's proposal with the ntag424 DNA (the same NFC chip as in a bolt card) and a remote signer. Works well.