How would you redirect calls to the top object in Cypress?

In my application code, there are a lot of calls (like 100+) to the "top object" referring to window.top such as top.$("title") and so forth. Now, I've run into the problem using Cypress to perform end-to-end testing. When trying to log into the application, there are some calls to top.$(...) but the DevTools shows a Uncaught TypeError: top.$ is not a function. This resulted in my team and I discovering that the "top" our application is trying to reach is the Cypress environment itself.

The things I've tried before coming here are:

1) Trying to stub the window.top with the window object referencing our app. This resulted in us being told window.top is a read-only object.

2) Researching if Cypress has some kind of configuration that would smartly redirect calls to top in our code to be the top-most environment within our app. We figured we probably weren't the only ones coming across this issue.

If there were articles, I couldn't find any, so I came to ask if there was a way to do that, or if anyone would know of an alternate solution?

Another solution we considered: Looking into naming window objects so we can reference them by name instead of "window" or "top". If there isn't a way to do what I'm trying to do through Cypress, I think we're willing to do this as a last resort, but hopefully, we don't have to change that, since we're not sure how much of the app it will break upfront.