Weird...
Pierre will only go poo (when we are home - when we travel we are fortunate to have a much more easy going dog) in his 'rock garden.' We have a few empty lots next to our building - and it being Florida, much of it is sand. There is a part that has rocks (which is nice because then I don't sink into the wet sand) and there is the only place we can reliably get him to go.
And for Duncan (he is almost 11 weeks, so earlier in potty training), I pick him up out of his crate and carry him until I set him down outside. Then he only has to walk a tiny bit to a patch of grass he fancies. If I put him down before, he isn't reliable about holding it. Of course, I wait for him to whine to get out, so he already has to go.
I would restrict her water as well as feed very consistently. I had to do this for Pierre. He got it at meal times, right after playing, and when coming in (again, it is Florida - quite hot). After timing it a few times, I got a window of when he would go. It was a wide, somewhat sporadic window, but once I knew it, I could take him out to fit his needs. He did not go in his crate.
Instead of crating her while you are awake, I agree with the tethering thing. Just put her on her leash and tie it to a belt loop. I've seen 'umbilical' ones that do well. That way, you can get used to her signs and catch her before or in the act.
Perhaps she is going in her crate to get attention and out of the crate. What do you do after she goes? Do you let her out because you know she is on 'empty'? If so, you may be reinforcing the behavior. "Gee, if I go in here, I get to go out there!" Think about your routine and how it seems to her. You may be doing everything right, I'm not there. It is worth analyzing, though.