But, what I was thinking of is that you could fully configure your ship (ship type and load-out) before the mission begins. So you would effectively have two (or more) customizable ships to switch between at your discretion during the mission. This can't be done with just events, no?
Yes. Use fighters in, say, Gamma wing to represent the player's alternate vessels. Have them spawn in the mission at a vast distance, stealthed and hidden from sensors. Use variables to transfer the loadouts and classes of these alternate vessels to the player's once he switches ship types (you could have him pick from slots, each of which would be a preconfigured ship).
I'm not sure what you mean by the menu... could you elaborate?
I'm not sure how much more I can elaborate. I was saying that it is possible to use good FREDding to construct a menu, using training messages or subtitles, by which the player would select their new ship and weapons.
For extra bonus points, pull a trick from BP's FRED toolbox and add a point system that the player can use to buy better ships and weapons in-mission. You could earn points with kills or whatever.