When you save ship designs in the ship editor, it doesn't save with the ship the miniaturization lvl that you used to build the ship. (For example, advanced vs basic).
So, what you can do is, research all the miniaturization techs, then design some small ships with low level weapons / defense, start a new game, research just the weapon techs, and have beefier-than-normal ships at (near) the start of the game.
I first noticed this when I could build a small ship with 2 missle attack and 1 shield defense (tiny ship, that I had designed in a previous game), but couldn't design the same ship.
Edit: Loving the game, by the way.