Hey there I would definitely remove the care fresh from the cage, it is probably only confusing her as to where she is supposed to be going to the toilet. Once you remove that it should be easier to get her more consistent with the box. After she’s been spayed and has had good litter habits for a while, you could probably put blankets in the cage without trouble, but I wouldn’t go back to bedding like carefresh, it’s a bit too similar to litter.

Well she’s still going to pee outside the box until she learns not to, but it does take time. The best you can do without bedding is to wipe up the pee as soon as you see it with a paper towel and put the dirty paper towel in the litter box. Then spray and wipe the area with a vinegar/water solution to remove her pee smell. Litter training is going to be much harder leaving bedding in the cage in addition to the tray.

You could certainly start now, the sooner you start the easier it should be to break bad habits. Although if you were concerned about wasting the left over carefresh you may have, you could continue how you are until it runs out or after she gets spayed, it likely won’t matter too much either way. Unspayed rabbits are often harder to litter train, so if it’s only a month or two until she is getting spayed you could just wait until after and you will likely have more success.

I definitely agree with azerane. Having bedding all over the cage will confuse her as to where to go. I definitely recommend just the litter box. She’s probably peeing outside of the box still because she’s kind of been trained to pee on the floor of her cage. She probably just needs to be litter trained. Here are a few videos on litter training your rabbit: https://www.youtube.com/watch?v=t7mEUn2Jsa8  
https://www.youtube.com/watch?v=JKevuEvgfyM hope this helps you out!