It sounds like you have mostly sorted things out! Sorry just seeing this now.
Spaying/ neutering (for both buns) is very important for successful bonding, so the plan to get her spayed is a good one. Then you should wait at least 3-4 weeks for her hormones to settle. I agree that cage swapping is great, but I think waiting till after she’s healed from her spay is a good move. While they are hormonal they smell different, so all the swapping will probably just mean you clean up a lot of pee and poop because they will be marking all over the place.
Letting the new bun settle in to her new home is also usually really helpful to a strong bond forming.
I would read through this info since you are new to bonding: https://binkybunny.com/infocategory/bonding/
There are many ways to bond rabbits, but some can be quite stressful for the rabbits and a bit dangerous if you are inexperienced with rabbit behavior. The info summarized in that link should give you a good starting point, and you can post again once you start pre-bonding to update us on how the buns are doing. 🙂
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.