1. The blackberry mush and water will add carbohydrates to a small degree. It definitely won't hurt anything.
2. You can transplant anytime you think she needs it. The two biggest issues are:
1. Is too late to make any real difference? If you don't think she has but a couple of weeks, then leave her in the container she's in.
2. The other is how gently she can be moved from one container to another. For example, you'll want make sure you water her really well right before you lift her out. This will help to keep the dirt stuck together making it less likely that you'll break root tips when you lift her out. If you think you might drop her, or otherwise seriously disturb the root structure, then leave her where she is. As for HOW you take her out of the current container....the least disruptive way I know is to place one hand on the top of the container covering the top layer of dirt with the stalk sitting between your fingers. Then carefully turn the entire plant and container upside down. With the hand that is not holding the stalk, gently tap and squeeze the container (if possible) while trying to GENTLY slip it off of the root structure. Once you have it free, place your free hand underneath the rootball, and GENTLY set her in her new container. Of course you will have already put new dirt in the bottom of that new container before you started all this.........sorry, forgot that part above......lol.
That's how I do it. Others may have better advice, but this works for me and I NEVER break roots this way.
Let us know what you decide to do.