60 degrees is too warm for real torpor to occur.
If we’re talking wildcaught box turtles (seems to usually be the case), where did they originate? Many specimens in the pet trade hail from Texas (three-toeds) or South Carolina (easterns). You might have more tolerance from those specimens for extended periods at 60F (a temp at which neither proper active or inactive metabolism is achieved) than you will from animals that originate farther north.
Some specimens (even from one population) take longer to go under than others. Under natural circumstances, this is not a problem, since days can warm reasonably through October/November and permit some activity. However, in a dark basement where constant terms are forced upon the animals without daily variation in light and temperature, box turtles will lose control of their regulatory abilities. This is the best way people have and likely always will encounter difficulty in reptile management – by inadvertently miscontrolling of their inmates’ regulatory abilities.
The answer to the eastern’s problem was posted synergistically with the question(s) – things aren’t working for the eastern, so consider other options (alternate mode to induce hibernation, continuing a light cycle till temps drop further to permit some daily warming, etc.).