Hi Alex,
I just obtained the latest x737FMC for the x737 Project 737-700 and 737-800, for X-Plane 11.11. This FMC does not load X-Plane flight plans now in 11.11, but support is planned in the future. In the meantime, Javier, the developer of x737FMC (which is really something!) says that it will take UFMC format plans.
How hard would it be to make Little Navmap export to that format?
Along with the large number of export formats you now support, Little Navmap is starting to become a universal format converter!