You should not never "need" levers to move a belt across cone-pulleys. That risks damaging the flanges and suggests the belt is a size too short for the machine.
The machine should have a method for readily releasing the tension at the motor end; by allowing inwards movement of the motor on a hinged plate.
Once done, ease the belt off the smaller diameter first. Move it to the larger of the selected new pair then ease it over the smaller.
Mind your fingers!
Always leave a little slack in the belt. It should be possible to push the middle of the longest leg of belt by finger-pressure inwards by maybe half an inch, before the resistance increases markedly.
A two-stage reduction often lets the centre pulley cone mounting float on a swinging-arm (as on the Myford VMC Mill), but on some including the Warco mill/drill it is mounted on an adjustable plate held by gripper screws. On such mechanisms:
. – Slacken both sides of the drive.
– Move the belts as required.
– Tighten the secondary belt (to the spindle) first as above by moving and re-tightening the idler mounting,
– then tighten the primary (motor) belt by its motor adjustment.