Upon further consideration I have determined that the US:UC market cap ratio will reach equilibrium according to the profit provided by the system. The higher demand for UC, then the greater the profits. Demand for UC would encourage US->UC conversions which would reduce the supply of US but increase the demand for US thus increasing the price of each share. But increased profits from fees would provide additional demand for US increasing its market cap.
If UC demand fell then it would promote UC->US conversions which would reduce the supply of UC and increase the supply of US, but the price of US would fall, and the price would fall additionally due to lower profits and the market cap will fall.
Therefore there is no need to regulate a US:UC market cap ratio as it would reach equilibrium according to the desired PE ratio (plus speculative future earnings) where earnings are dependant on UC demand.
Instead of burning fees to allow US->UC conversions to increase the share price and provide profits in a roundabout way, it would be much easier for shareholders to understand if all revenues were placed into a business account. From this account shareholders could 1. make payments to cover expenses and 2. distribute UC to themselves as dividends. It would be very easy to record revenues and expenses this way. Alternative revenue sources (such as exchange fee-sharing) could be provided by sending revenues to the account.
The more I think about it, the more I realise the system ought to self-regulate very nicely, making the entire focus for shareholders around reducing costs, and increasing revenues.
Edit: I’ve just changed the original post significantly upon further consideration of the economic model.