I wouldnt get too hung up on the ratio issue. UNless you're on the margins just near enough is good enough. By way of example, a 20tooth pulley on a 5mm pitch belt has a circumference of 100mm (20 x 5) and a radius of 15mm.

Assuming your gantry weighs in at 20kg you need around 5g acceleration for accurate path following, so the force you need is 20 * 5 = 100N (which suggests you could get away with a 10mm wide belt, max 350N per 10mm width) Your motor is driving the belt at a radius of 15mm so the torque required is 100N@ 0.015m = 1.5Nm - now this isnt the static torque of the motor, its the torque required at full speed. If you have a 1.5Nm holding torque motor, you need to gear it down by say 1:3. Driving the belt pulley with a 45tooth needs a 15tooth on the motor. Assuming a maximum of 300rpm on the motor gives a maximum of 100rpm at the belt = 100 * 100mm/min or 10m/min for rapids (on full step) and a maximum resolution of 100mm/(200 * 3) = .167mm (on fullstep)

Of course you can go to lower gearing with lower acceleration as long as your cutting speeds are lower as well. You'll need to work this through for your own. The tricky bit from a construction perspective is the driving of the 20tooth belt pulley from the 45tooth one as the 45tooth is larger (and would probably be outboard of the belt to avoid having a slot in the bed.