Having had a kitty who was "DKA", I know ketones is not a place you want to go back to. At this point, letting her eat grilled or anything she will eat is what you want her to do.
The "recipe" for ketones seems to be -
Insufficient insulin + insufficient food + some type of infection.
If she will eat higher carb food, that's better than not eating. At least it will allow you to more confidently give her insulin.
I think I would see about a different vet if you don't feel this one is communicating well enough. A 4u dose this soon is pretty radical, but I think the vet is trying to do whatever she feels is necessary to get the BG numbers down. It's a tough call when you are trying to juggle getting the numbers down and trying to make sure there is food on board so the numbers don't drop too much too quickly. And her having ketones recently is another big factor, because that makes everything even more complicated.
And definitely, you want to be able to monitor her blood glucose with a meter you have faith in, so yes, try to get one that works for you.