LBR and baserunning responsibilities

[youngump]

So Dakota's post on the LBR got me thinking about something I don't know if I understand completely.

R1 at 2nd. On a ball hit to right field she leaves ball is popped up. As soon as the catch is made, the ball is thrown into the pitcher by an inattentive F9. When R1 gets to third she stops. She now cannot return to 2nd unless the pitcher makes an attempt at a play. Being a smart, pitcher she instead wants to make an appeal.

Here's where my conundrum comes up. I've been told that if the pitcher is going to make an appeal to call the ball dead so as to avoid an error in the live ball appeal process. Now, what if as soon as I call dead ball, the base-runner breaks for 2nd to "complete their baserunning responsibilities" (now that she can, since before she was forbidden by rule from doing so).
If I don't allow the runner to return than the dead-ball gives the offense some advantage here. On a live ball, the runner would be able to try to get back to second and hope for a bad throw once the pitcher started to make the throw.
But if I do, the DC is going through the roof about my calling the dead ball.

So my sense is just to call the dead ball, accept the appeal immediately and call the runner out. But can this be justified from the book?
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Laguna Bay Condominium