You are correct the fillets at the top are causing the difficulties. A general strategy is to avoid adding fillets until necessary.
Another very useful strategy is to incrementally save your project so that you can go back to an earlier version. Then you can either back-up to an earlier version, or open an earlier version to retrieve a component. I start by adding two or three digits to the file name the first time I save a project; for example Skiff001. (Note, commands are from Rhino for Windows.) Then after making significant changes that would not be easy to reverse I use SaveAs and increment the name to Skiff002, and repeat after signficant changes. I also frequently Save in between significant changes so that I have a current copy available.
An approach for your current situation:
DupEdge for edges of the large surfaces around the opening (not the fillet edges).
Connect to close the gaps.
EdgeSrf using the new curves for a surface.
Try using Trim to trim the corners of the new surface to the fillets. You wll find it doesn’t work.
ExtendSrf for the fillets.
Trim the new surface and extended fillets to each other.