If her poop is normal when you eliminate fruit, veggies, and treats, then it's safe to say one of those is the cause of the mushy cecotropes(cecal dysbiosis). Which means that which ever is causing it will likely need to be eliminated from her diet permanently, or at least for some time to give her gut microbes a chance to get back into a sustained balance. It may be some foods were introduced too quickly and her gut bacteria didn't have adequate time to adapt, but also possible she is too sensitive and can't have the offending food(s) at all. Some rabbits are just more sensitive to some foods and can't have them in their diet or it will always cause problems.
Most likely culprit would be the fruit and oxbow treats(high carb). Veggies would be less likely, though not impossible. If she is still having the mushy cecals with fruits and veg removed, pellets or the fresh grass could also be contributors. I've had a few rabbits that were sensitive to pellets, fruits, and any high sugar/carb food, and couldn't have them in their diet at all. Fresh grass, particularly early young growth that can be too rich, can cause problems for some rabbits.
I would start with removing the fruit and oxbow treats(and any other high sugar/carb foods, eg carrots) and see how that goes. If it's still happening with the veggies, it could just be the types of veggies you are feeding, so you may not need to eliminate all veggies. Usually the leafy veggies are the least likely to cause this kind of problem, when not fed in excess. High starch veggies(eg carrots) or ones with high water content(eg cucumber, celery) can also sometimes cause issues.
Here's some good info on cecum problems and cecal dysbiosis if you haven't seen it already.
Intermittent Soft Cecotropes in Rabbits | House Rabbit Society (cecal dysbiosis)
Disorders of the Cecum | House Rabbit Society (disorders of the cecum)
Though bathing a rabbit is highly discouraged in most instances, sometimes butt baths are necessary for rabbits with health issues that are causing cleanliness problems, as this can pose a fly strike risk. Though if a butt bath is done it always needs to be done correctly and with caution(best to consult vet).