What is the best way to make Vicks and Wedge into "normal" party members?

Long Answer:
Well, I am helping work on the ASM for the 15th Man project, which will eventually add a full character to the roster. If we are successful, putting Wedge/Vicks in the cast without replacing existing characters *should* be doable. If you intend to keep the Soldier sprites for them, it may even be trivial. We are still pretty early in the process but so far there is nothing foreseeable that will totally block us from adding 1-2 new characters. There are still some questions as far as unique magic lists and whatnot, but there are partial solutions for even these that are less-than-ideal, but functional. It's just a matter of putting in the work. When the 15th Man project is finished, there will be a patch for adding them, plus I will probably make a detailed tutorial on how to do it yourself... expanding the ROM with FF3usme will be a requirement.

Short Answer:
Play my upcoming hack.