"Will make a very big difference just the belt drive"
True - the thing that excites the noise is the gear teeth both hitting each other (physically) and air being squooged out of the tooth area at noisy velocities.
Both of these can be reduced by helical gears - but at the cost of end-thrust. (Hence double helical or herringbone gears).
Breezy - I can see you are a thinker and experimenter
You could try friction belt drive using turned pulleys from wood and a belt cut from bicycle inner tube or similar!
Or you could use the same mount structure as for the gears but fit belt timing pulleys (about 1.7 to 1 ratios - so long as they miss each other) and fit a third pulley (doesn't need teeth) to take up the tension (mounted somewhere out to the side)
Hard to describe - will sketch if it would help. There is no need then to find a matched toothed belt
andrew
rob an old printer - they used to have them in the paper drive!