Adam, I honestly think you are overthinking this one. We have a specified time period to deal with an injured/bleeding player. The coach can extend that period by calling a timeout. At the end of that timeout, the player is either ready to go, or not. If ready - away we go. And that includes calling another timeout if they want to.
If not ready, though, we now have a procedure to follow to get a sub in for that injured/bleeding player. And that procedure needs to be followed BEFORE allowing anything else to take place - including calling another timeout.
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