Okay, in reverse order of apparent difficulty:
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Use a cable to connect the tripod-mounted rig to the SLA on the floor;
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Try the AAs, but be prepared to abandon the idea if it doesn't work;
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Reduce the stepper motor current until it no longer keeps synchronised, slowly increase it until it moves reliably, then increase it by a further 33% for safety;
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Calculate the largest acceptable angle you can move and still have the motion imperceptible in the final footage, then change the stepper and gearbox to the lowest current pair such that this angle is moved by 4 full steps of the motor;
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Go back to the drawing board and design in a tiny geared servo motor with an encoder, which will draw only the current required to make the move.