This game works decently for me except for one thing: the mouse sensitivity in-game is too high.
I tried to change my default settings in the control panel but that does not seem to affect the game.

Yeah I have this too. Didn't look for a fix yet though. If I find one I will update

There are not any mouse fix, in fact there are not any tool or mod for Port Royale series, but i am building a community and i am working on a mod tool for a Port Royale and Patrician

This is my facebook group https://www.facebook.com/groups/478150129615434/

Recently I learned about this issue. Movement is FPS related, that's why it moves like crazy since the FPS is around 900-1000 for new systems. It should be 60 for normal movement speed. AMD or Nvidia settings cannot cover this so you need a third-party program. Some guy suggested me this: "Guru3D RTSS Rivatuner Statistics Server". After installing, you basically add a profile for Port Royale and limit the FPS to 60. After this it should be fine.

I recently made a tutorial, have a look, if it works then great.
https://www.gog.com/forum/port_royale_series/how_to_run_port_royale_1_in_windowed_mode_on_windows_10_and_fix_for_fast_scrolling