Hi. I think you're locked in a tautology. If "transactional utility is the price of money itself" then it can only be determined in relation to that which it prices itself by, i.e. its own unit of currency or an equivalent. Assume for a moment that this "transactional utility" amounts to one billion US dollars. What is the 'value' of one billion US dollars independent of the value of one US dollar? What is the 'value' of one US dollar? One and one billion are literally just numbers. They do not have any inherent value in and of themselves, and they certainly doesn't soak up a mysterious quality called 'value' just because we put a symbol in front of them
I didn't quite understand what you meant to say
Nevertheless, it looks like you are trying to present it as a tautology when in fact there should be none. Transactional utility is a real utility objectively arising from the convenience of using money over barter. Money doesn't spoil like crops, you can easily transfer value with it, exchange an arbitrary amount of some goods for it and then exchange it for an arbitrary amount of other goods at the time when you see it most appropriate. All these qualities (and a lot of others that I didn't mention) make up what is called transactional utility and what essentially makes something into money (since transactional utility is as inherent quality of money). And as such, it can be separated from money (money token) and assessed in money (money tokens), just like any other utility of something useful can be valued in money