So just a suggestion.
How about adding new Tomestones with no weekly caps but.... Make all the new dungeons only drop 15 Tomes per run. I would even say make it so no one can speed run the new dungeons. Add barriers like you did to stop people in AK, Make it so people can't skip mobs by locking them out with boss barriers.
And before anyone says that isn't enough tomes, Half the people on these forums complain because FFXIV is a Monday game. Yes it's grinding. But it will be better than capping and back in the same boat we are in now.
Also could add like 15 per day to duty roulette.
This would be even better.