The hotel (or any tour company) can book it but it will be cheaper if you deal with the driver directly. You will have to negotiate the price but expect to pay a bit more for stopovers. Because of petrol price increases and inflation, I’m hesitant to guessinate a price but, with good bargaining, I would think perhaps something in the neighbourhood of LE 500-600.
I am planning to do the same so this thread is helpful.
I would expect it to be 25% higher since that was what I pad a few years ago - Maybe I'm terrible at haggling!!