Does 'playing time' mean clock has expired or that the fourth period has ended? The rule is intended to prevent timeouts being successively called between the end of the regulation and overtime. I consider this as an extention of the 'playing time' and would without hesitation grant the timeouts.

2005/6 Casebook 5.12.3. TO after first one not granted for all free throws, as the "clock running" is the key factor.

Casebook 5.6.3 D confirms unnecessary free throws will NOT be attempted. If they are down 3 and the first one is missed, point to the table to confirm no issues (which may be unnecessary due to the delay caused by shooting the FT), take off your whistle, and get off the court.