I would replace it with FFV's battle system, rather than Tactics'. The fact that all characters (except Umaro and Gogo) can learn all spells without much difficulty is a large part of the reason the game is so easy. The Job system in FFV required a lot of work to master, and it wasn't really practical to have all characters master all jobs until at least the second world, if not the Void. It doesn't hurt that FFV was set up to be a much more challenging game, either.
Alternately, I would leave the current system but make it so most characters can master much less magic, depending on their starting job. Having all characters able to learn all spells removes a large part of the difficulty from the later part of the game. There is essentially no reason to use most characters' special abilities once they learn enough magic. The special abilities are just kind of... there.
A third option would be to use the job system, but also leave in the system where every character has a unique ability that no one else can learn.
Beyond that, I wouldn't go so far as to make Gem Box/Economizer/Offering require two relic slots, but I would probably nerf the Gem Box/Economizer and Offering/Genji Glove combos. Seriously, having the potential for five spells a turn cast for 5MP or eight attacks is just ridiculous.
Osmose needs to at least fail sometimes or something. There is no point ever conserving MP in the game as it exists because you can always recover it with minimal effort.
Runic is actually pretty cool, but as Alpha2099 said, the usefulness of the abilities is widely varied. I would balance the level of effectiveness between things like SwdTech (useless) and Blitz/Tools (way too powerful). There is also a glitch that makes it possible to spam Joker Doom in tool-assisted speedruns, but I might leave that in for the lulz, since most people won't be playing frame-by-frame.
I think they fixed Wind God Gau in one of the reissues, but it goes without saying that Gau as he currently exists is capable of being the most powerful character in the game. I guess that's to make up for his attacks being random and uncontrollable, but even so, he's still too powerful. Then again, so are basically all the characters in the game to a lesser extent.
Obviously a lot of the bosses should be way more powerful. Especially Kefka. For a final boss who had absorbed the entire source of magic in his universe he was disappointingly weak. I would also throw in the removed KaiserDragon as an optional boss (I think they did this in Advance, but I never played it).
That's a fair kickoff selection. I would probably do more things but those alone would improve the game a lot.