You know I've been considering this definition of yours and I don't think Labor exchange is really the defining quality of money. Simply consider the case of an economy ware no one is a wage earner, everyone is self employed and sells goods or services to each other (such as a butcher, a backer and a candle-stick maker). No one pays or receives wages but money is self evidently possible.
Rather I favor the definition as "A universally accepted extinguisher of all dept in a society", now the universal part is key because that means it's accepted in payment of taxes and in reality taxes will always be the driver behind a money system. Any society with enough complexity to need money is going to have some kind of taxation even if it's very informal like "The chieftain calls upon the people to give", and you need to have some liquid token you can pay that debt in. And once the chieftain will take it then everyone else will too because everyone's going to eventually have a need to pay a dept to said chieftain.
Sure in TODAY'S economy the buying and selling of labor is the single largest 'market' in the whole economy, so big we don't even recognize it as such and nothing could be considered money if it didn't exchange for labor but it needs to be bigger then that to really be money. If I could get payed in a token but not pay my taxes in it then its not money. Many old turn of the century mill operators would pay employees with some kind of company script that was not usable to pay taxes and was not by my definition money (such practices are fortunately outlawed now).
I didn't either until I sat back and considered that the hypothesis of labour is the foundation of all economic activities. Without it alone, nothing ever "happens".
Your butcher must obtain handle and store carcasses, carve cuts of meats from them, sell them and package them for his customers and pay his store's bills etc, regardless of wether it's just his name over the door or not. Bakers and Candle makers are no different. Hiring somebody to do your job is labour too, just like shopping for a house or a car is. Not all "labours" are rewarded and certainly few are "equal" but that does not impact on their "values". Indeed the costs of all labours needed to produce a product are not and often need not be reflected in it's price, as when a Cadillac AC system finds it's way into a cheap Chevy
Doesn't a great stock pick "cost you more" because you had to do more labours finding out about it? Even pushing a button, firing a bum, selling a
BTCitcoin or finding a fishing lure is a labour. Most labourers have to do 5 or 10 labours a day before they can even get out of the house to go off and slavishly "bruncheon" in their boardrooms.
Indeed many labours are not actually even "productive" in most any regard. Most tank and ICBM and bomb makers still nonetheless produce outputs that have intrinsic, utilitarian and most definitely value-added "exchange" values regardless of the market demands of those who depend upon or "benefit" from their uses...
The sort of tax-money you speak of was already invented by King Henry 1st back in the 1100 it was done to foil the counterfeiting bankster-goldsmiths and built Britain until the Rothschild bankster coup in 1826 finally pushed it back into abject economic "counterfeit rented-gold-debt receipt" slavery.
Around 1100 AD King Henry 1st resolved to take the power of money away from the lenders. He invented one of the most unusual money systems in history. It was called the Tally Stick System. This system lasted until 1826. The Tally System was adopted to avoid the monetary manipulation of the goldsmiths. Tally Sticks were merely sticks of wood with notches cut on one edge of the stick to indicate denominations. Then the stick was split lengthwise so that both pieces still had a record of the notches.
The king kept one half to protect against counterfeiting. The other half would be spent into the economy and circulate as money. Under this system money could not be manipulated, and it could not be stolen. No other form of money had worked as well, and for so long as Tally Sticks. The British Empire, which was the most powerful nation in the world, was built on the Tally Stick System.
Henry was the first dude to figure out the best reason to "also" make a "money" represent something else that it was not.
...And he was no doubt greatly pleased to see "his slaves" spending all those "tax receipts" of His, too.
In every part and aspect of all economic activities you will find and/or exploit the hidden values of past, present and/or future labours.
The PRIME RESOURCE of "all labours" is what an "economy" is. All else is just "stuff labours bring or do with them".
Even writing you this answer is a labour, but you certainly earned it LOL