I think the same feel of DoT gameplay could be easily achieved using a gauge-focused job instead. It really just boils down to timer management, but without the risk of maxing out debuffs on the enemy and the other associated problems DoTs have in this game. I'll use a Chemist idea I've had as an example for ease of terminology:

First, a single marker/conduit is placed on the enemy, similar to RPR, or as an offensive Kardia. This marker does no damage on its own and has no timer on it. Another way to think of it would be dance partnering the enemy. As you cast your "DoTs" the target of your conduit begins to suffer damage. Like with a dance partner, only one can be active at any time. An AoE version that overwrites and is overwritten would also available to balance potencies in AoE situations.

The job gauge, which determines how much damage the conduit is inflicting, is made up of several vials/flasks/beakers (3 or 4). Each time you cast your "DoTs" on the enemy, your really just filling your vials. Each vial could have its own size/shape that helps to reflect its duration (multiple timers of differing maximums is usually desired in DoT gameplay). These vials would begin to drain into a reservoir.

The reservoir would be a secondary gauge used to do the standard DoT interactions such as refilling all vials at once, or to use that mixture of chemicals into a high potency attack. When a boss invulns, the vials are continuing to drain into the reservoir so there aren't any "wasted ticks" during phase changes. When the boss is about to come back, you could use the refilling ability, and refill each vial proportionately while consuming the entire reservoir (something like 100% full reservoir would refill every vial by 50% to encourage their future maintenance). Maybe include a vial emptying ability that lets you fully drain all vials to max out the reservoir instantly for 2min burst windows. There's really a lot of options that open up when the attention is diverted to the job gauge to create a sustained damage over time job.