This would be an interesting run, indeed. With luck manipulation, you'd be able to avoid most or all "random battles".
Personally, I'd suggest LUX (the tetujin) and either Kamil (the warrior human) or Olvan (the dwarf) for their high strength and defense, choosing LUX over one of them for financial reasons. This will also facilitate a couple of the more frustrating parts of the game:
(1) The Dragon guarding the Sky Rune: This dragon pretty much requires that you use Fire Magic on it, if I remember correctly. Olvan's or Kamil's Fire 1 (you probably won't have Fire 2 yet) will be helpful here, as well as any B Fire you find.
(2) The Curse of Silence: Without Apprentices that depend on their magical ability, Metal Pison and the rest of this part of the game shouldn't be as difficult or slow.
At first glance, it appears that Agility will be your most important stat, as dodging attacks completely will probably be a necessary tactic for survival. Defense + Double Attack will probably be your primary means of doing damage as well.
Overall, I bet this game would make for an excellent TAS, and maybe not unbearably difficult to luck-manipulate. From my very limited testing, it would seem that dodging random battles and enemy attacks might be possible by pausing for X amount of frames while walking or before selecting "Attack" or "Defend".
As enemies shown in the Crystal Ball reach the row or column you are in and continue approaching, they seem to make a >^>V>^>V> or similar pattern, so dodging enemies that are following this pattern might be as simple as timing your movement to pass them while they are one row (or column, as the case may be) to your side (pausing for a frame or few frames while walking may be the quickest way to do this). As for dodging attacks and ensuring that yours connect, the luck manipulation may be able to work out similarly. Try attacking (or defending) at a certain frame, and see if your attack lands and your enemy's (or enemies') attacks miss. If not, go back, and wait an additional 1 frame before attacking.
I haven't tested this at the frame level, and even then, only to a limited amount, but I hope it can get ya started!
P.S. Wilme gets no armor... except the loin cloth they added in the US version... and the only weapon he can equip isn't something I found until I read a FAQ. His magic is the weakest in the game, but now that I think about it, might be sufficient in a TAS in comparison to Olvan because of the increased Speed he has over Olvan. Good luck!
</ramble>