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.
My opinion is he used the wrong words.
"transactional utility is the price of money itself" SHOULD BE "transactional utility is the value of money itself"
As money is always acquired to be exchanged later for something else, its value is in the ability it confer to obtain some other good and service in the future.
This, in exchange depend on its features and how many people use it and how often.
Menger explained money as the "more re-sellable commodity" available in the market.
Mises, explaining the Regression Theorem, state gold (or any form of money) INITIAL value is the value of direct use at the time it is used for the first time as a mean on indirect exchange.
As gold started to be used as a mean of indirect exchange, the price (the exchange rate of gold measure in other goods and services) raised. This can be understood as the same quantity of gold was used before only for direct use (jewelry, etc.) now must be used for indirect exchange and some direct use. So the less valuable direct use must be ceased to free some gold to be used as a mean of indirect exchange.