Why not just make everyone a DPS?

[Reynhart]

But here's the real rub, if you start making tank mitigation super important (even though it is still being checked), WARs will simply take the place of PLDs on the sidelines.

You make both mechanics at the same time.

Let's imagine a big boss who create parts of him. Each time one part is killed, he loses a 10% of its life, and you need one tank for the main body and one for the part.
You could have any tank on the main body focused on surviving high damaging moves (So, any tank with high VIT, but "mostly" PLD or DRK, since damage is less relevant), and one tank on the spare part focused on dishing out damage (So, any tank with high STR but mostly WAR since surviving is less relevant)

You could even alter the main target to switch periodically to either physical or magical busters, thus each tank will have its strong and weak points in the long run, and the spare part to switch between physical and magical resistance so that you want to mix your DPS.
For an additionnal mechanic, you could make the body to keep only one type of busters (physical or magical) when it hits 50% HP, thus managing your timing so that the final from better suits the main tank you have.