Mask it with quest-based progression that is more than "kill five marmots and bring me their hides."

Things like Toto Rak and Darkhold are a good template, minus the speed run thing.

A good game would have something like Grand Companies. Based on your level, the company would allow you to investigate certain dungeons. Explore the dungeon while getting exp, fight an end boss for bonus exp, get extra exp from the GC if you win all dungeons in a level range.

Then tie it all into the storyline. Have what happens in the dungeons play into the next big mission.

This system could take months to arrive at cap, but it'd at least feel like actively playing the game. My problem with killing the same mobs over and over is it feels disjointed from the rest of the experience. There's no real reason to be doing it other than that you have to.

The best part of old FF titles was just that. Leveling was paced to happen on your way to the next town or big battle. That's part of what made FF what it was just as much as Moogles and Cid. The feeling of always moving forward.