I love having enchanted weapons, but I loathe the fact that I constantly have to be refuelling them with soul gems. I am running MGE right now as the only mod for Morrowind, and this is really the only thing that I really just want to have as a mod.

To be clear, I just want a mod that removes the "on strike" charges that weapons have. I feel that if I enchant an item, that should be it, no more finicking with it to "recharge" it. I just want it to be fully enchanted forever with no penalties.

I don't think there is.... Unless you alter some GMSTs... but this is the easiest mechanic in the game to bypass.
All you have to do is wait, and they refill themselves. Anytime that you can, just wait/rest for 24-72 hours and most enchantments will be refilled to max.

Using soul gems is the slow way, but it does increase your Enchant skill.