Great question! One of the (extremely few) downsides with FROST is that you have to choose which signers will be participating at the start of the signing session.
The signing quorum signs under an agreed set of nonces belonging to the signing participants:
In this case, {nonce from device "Stay", nonce from device "Frosty"}
and you can't change this halfway though the signing session.
You elude an interesting idea though, the app could auto-detect at least the first signer and only make you select the other t-1 signers.
