We hope to use FORTRAN to re-code the calculations as library routines, called from a GUI interface code in another language.

This plan would be far more feasible.  If you're planning on building a library in Fortran to be called from another language, I have two major suggestions:

1. Only compile for 64-bit - 32-bit-only operating systems are disappearing.  The calling conventions for 32-bit code, notably on Windows, are varied and nightmarish to deal with.  64-bit code generally all complies with a single calling convention regardless of the compiler used.  You won't have to dance around with strange Fortran preprocessor directives forcing "STDCALL" or write aliases to Fortran functions.

2. Commit to using the Fortran ISO_C_BINDING module - every language can call C routines, generally.  If you declare C-compatible Fortran procedures that are "BIND(C)" with C-compatible argument types, you'll save yourself a lot of headaches and end up with a truly portable library.

As for which GUI option to use, it again depends on what you're trying to achieve.  If you're just on Windows, C# and Windows Forms would be a nice option, or you could even consider our AppGraphics package if you don't mind working with a decidedly small subset of GUI components.  If you're going cross-platform, Qt with C++ or Python with tkinter are both great options.  IUP is a nice, light option as well.  Some people like using Gtk-Fortran, but I find it generally too heavyweight and unwieldy.  Some of the newer, simpler GUI interfaces like Dear ImGui in C++ might fit the bill.