I Reached Crystal Using Only BLM. AMA.

[Raistlin]

Yeah, like I said earlier, I think the easiest and most appropriate change is to make the DoT increase in potency with more stacks instead of duration.
It gives you a tradeoff between control and burst damage, and the DoT ticking off more quickly mostly solves the issue of reapplication being worthless.
The OP's suggestion of having a reapplication of Fire consume the existing DoT and deal its damage all at once is also a good one.

In FFXIV dots ticks on a fixed 3 second timer, u cant make them faster without changing how the game works, doubt is possible.