Firstly, price is not defined as necessarily monetary, though it usually is understood to be monetary value of an item. Perhaps, that's the price you pay for using a flexible language like English. See:
In ordinary usage, price is the quantity of payment or compensation given by one party to another in return for goods or services.
In modern economies, prices are generally expressed in units of some form of currency. (For commodities, they are expressed as currency per unit weight of the commodity, e.g. euros per kilogram.) Although prices could be quoted as quantities of other goods or services this sort of barter exchange is rarely seen. Prices are sometimes quoted in terms of vouchers such as trading stamps and air miles. In some circumstances, cigarettes have been used as currency, for example in prisons, in times of hyperinflation, and in some places during World War 2. In the black economy, barter is also relatively common.
A value that will purchase a definite quantity, weight, or other measure of a good or service.
However, if we are looking for a term that expressly excludes monetary payment, and want to be unambiguous about it, the only option seems to be non-monetary payment, as in "...non-monetary payment is the best way to compensate authors for the use of their words and ideas."