I Reached Crystal Using Only BLM. AMA.

[Iyrnwaen]

I think 3k-4.5k-6k DoT for 6s or 3k-6k-9k additional burst dmg sounds ok (perhaps a bit lower?) as BLM has no CC or stackable DoT during Fire, unlike other jobs which still have access to CC. This way, BLM can be a dmg dealer with Fire in a low dmg team comp, and can be a CC support with Ice for low CC team comp.

I love the concept of Fire and Ice being the exactly opposite, so i think fire should be pure in damage and fast for zero utility it has while Ice is already good in utility and dmg wise. If the devs intended to separate Fire and Ice, unlike RDM which can easily switch back and forth, making both of them viable depending on the current team comp might be a good idea.

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.