I feel like there's an easier solution than those suggested.

Remove the requirement to have completed "Sylph-management" in the MSQ before a job can be unlocked.

Very few players are intentionally not unlocking their jobs or not equipping their job stones. Most of the time, it is newer players unaware that unlocking the job is the normal next step for their starting classes.

With the abundance of XP bonuses available plus a new player's natural curiosity about side content, it's a rare player that hasn't reached level 30 (if not much higher) on their starting class before they choose their Grand Company. That means their class to job quest progression gets interrupted with no special reminder from the game to revisit the class guild once Sylph-management is completed. All that happens is the first job quest appears in small print at the bottom of the MSQ tracker where it is easily missed, ignored or not understood as significant.

Let players unlock the job as soon as the level 30 class quest is completed, no wait. Make it a smooth progression instead of something interrupted that the player has to remember to go back and do later. Get them in the habit of having the job stone equipped before they reach MSQ content where it actually matters.

In higher level content, treat classes like BLU. If a pre-formed party wants to queue together without job stones for giggles and a little extra challenge, let them. But don't allow players to queue without their job stones equipped if there is random matchmaking involved.