How can I migrate my blueprints between differently named C++ projects?

This wont solve renaming issue but it might help you switching up to new renamed module

Copy code module (folder in Source) from old project and then edit uproject file (in text editor):

"Modules": [
    {
      "Name": "RenamedProjectModule",
      "Type": "Runtime",
      "LoadingPhase": "Default"
    },
    {
      "Name": "CopiedOldModule",
      "Type": "Runtime",
      "LoadingPhase": "Default"
    }
]

and both *.target.cs files of new project

ExtraModuleNames.Add("RenamedProjectModule");
ExtraModuleNames.Add("CopiedOldModule");

…to add new module from old project

Now regenerate project files and build, this should make old blueprint work as old nodes will be active in new project and you can swap nodes and reparent . Ofcorse there might be issues if you got classes with same names in both modules

And in the way you learned how to make new modules which might be useful knowledge in future:)