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It appears you asked the same question in the Caravanistan forum. All of this answer will be based on the info there but since you seemed not satisfied with it you should come back here after your trip and give an answer based on your personal experience.
As reported in the forum post, there are ATMs in Beyneu so you can always withdraw some tenge. I also see at least two banks on Openstreetmap so you might also be able to exchange if you prefer.
Caravanistan also features a page on money in Kazakhstan. It says
ATMβs (bankomat in Russian) are found on every major street in big cities. You can withdraw money with Visa, Mastercard or Maestro. The occasional refusal of your card is to be expected, but most ATMβs accept a wide range of foreign bank cards. In smaller towns, there probably will not be an ATM available for cash withdrawal.
I'm not sure if Beyneu qualifies as a big city so that one is up for judgement, but it also says:
Currency exchange in Kazakhstan can be found on every street corner. Rates are competitive, once you leave the airport or train station. Main currencies that are traded with tenge are US dollar, Euro, British pound, Russian rouble, Kyrgyz som and Chinese yuan.
so you will find some way of getting enough tenge I'm pretty sure. If not, as pointed out in the forum, you should be able to pay your ride with dollars at a less advantageous price.