Converting Launcher/Binary-based project to use binaries compiled from source?

Everything that you have been doing should be working. There are a few things that would be good check.

When you run UnrealVersionSelector-Win64-Shipping.exe, do you get a “Registration Successful” message when it completes?

Do you have admin rights when you run the executable? Have you tried running it as administrator?

Does Windows have a file association already in place for .uproject files? Right click on your .uproject file and select Properties. Does it show “Opens with: Unreal Engine”?