Is it possible to implement formulas of my own design (such as those used to determine the damage output of weapons and abilities), and if so, how would I go about doing this?
Sure, by ASM hacking the formulas; they're hardcoded into the game code. There's a listing of the code for the formulas in the first few posts in this (http://ffhacktics.com/smf/index.php?topic=6538.0) thread (Click on the "Part 1", "Part 2", etc of fdc's posts).
If you don't feel like foraying into ASM hacking, you could request someone who does to write a custom formula, or something of that nature.
It helps if the custom formula you're requesting is something other people want to, and if you specify what formula you want replaced and what you want it replaced with.