Basically the most important part of my question is this. If I'm running a primary chain and secondary belt with the clutch on the crankshaft, will simply varying the tension on the belt vary the gear ratio? Or are my assumptions incorrect?
simply, with no jargon
NO.
you require a "variable pulley" which consists of two discs, held together by spring tension. belt rides on the outer diameter of discs for high gear (if this pulley is the DRIVER) and the discs spread apart on the shaft, against that spring, which then lets the belt ride near the shaft, or the inner diameter of the two discs, which will result in LOW GEAR.
the ideal setup is TWO such pulleys, as one gets larger, one gets smaller, and no belt tensioner is required! using only one variable pulley will require a belt tensioner, and also, the belt will experience some offset if only one disc moves. if both move an equal distance from the centreline, the belt will remain on the centreline.
you could use a single pulley, and vary the ratio by changing the belt tension, as long as the spring holding the two discs of the pulley together, is slightly weaker than the tensioner...
i used jargon, didnt i?
im sorry
simply reducing the tension on the belt alone will act like a clutch. and when it slips, you will burn your belt out. smoke, heat, squealing... think a car when the belts loose/worn out and its steering is turned to full lock. the belt will HOWL!
you NEED a variable pulley. be it the two discs that move together or apart (commercially available) or an expanding drum type (um....never seen one...)