Do you know if they are struvite crystals?
I just had a very similar problem with Rory. They found struvite crystals in her urine and also found that her urine was very concentrated and she had a pH of 8, and the vet wanted me to switch to a prescription food, which wasn't my first choice either.
I asked if I could try supplements instead, and the vet was comfortable with that. We added in Vitamin C and Cranimals (cranberry supplement) for a month. She also sent me home with Baytril just in case there was UTI, though her urinanalysis showed no infection. Also, I needed to get her to drink more water to help with her urine concentration level and since she primarly eats a raw diet (which doesn't mix well with water), I was going to add chicken broth (which unfortunately I could not find anywhere without onions or onion powder in it), so we ended up going with sea salt in an effort to get her to drink more. At her recheck, her crystals were gone, her urine concentration was better, and her pH was where they wanted it to be with a sample I took from home and also one they took in the office.
If it is only the struvite crystals, maybe you could discuss with your vet the possiblity of trying supplements for a little while and then retesting. I know the other type of crystals can require prescription food. And no matter the type of crystals, you definitely don't want to let stones form which can require surgery and be very painful for the dog.
I hope you and your vet can come up with a plan you are comfortable with for Khloe. Good luck!