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A large nescafe lid doesn't really sound that big or deep for a sand bath really, they do like to have a good dig around in the sand & some like to roll in & something larger might also encourage her to pee in it.
I have a similar problem with finding pee areas with Zen, it's such a small amount & the substrate is so absorbent it is hard to know where she's been other than the wheel & sometimes her sand bath, it basically comes down to checking her nest area regularly to see how clean it is or isn't & if Rosie is doing the same (not always peeing in one place but probably in the nest at least some of the time) you just have to keep checking, not too often though, weekly should be enough, just a quick look & only clean up what needs to be removed leaving everything else as undisturbed as possible.
If you can get her to come out for treats in the tube then you should be able to take her out for a quick check & minor cleans without the upheaval of whole cage cleans.
Her cage isn't that small so I think you could easily just do half at any one time.
It may take time & patience but do keep trying to coax her out before doing anything in the cage, if you remove everything & then try to get to her she'll know & already be scared.
Poo in the bottom of the cage isn't anything to worry about btw, you don't have to remove all of that at each cage clean, pee is what you really need to try to clean away.
Persevere with the food & treats in the box & hopefully she'll get brave enough again not to run off when you need to get her out.