Yes, it's actually kind of feasible to get a fire trial done in two days given just how quickly you can tear through mobs in Abyssea, but unless you were a BLU, if you were going to try to get it done that fast you'd need to hit basically every single Firesday until you got it done. Have fun planning several full 24-hour days of your life around not just FFXI, but one very trivial aspect of it.
Don’t bother camping fire weather; numerous people have tried and failed to do so in the past, so learn from our experience. Just hit Abyssea on Firesday when you can, kill as hard as possible for an hour, and keep in mind that you WILL finish it relatively quickly one way or the other and driving yourself crazy trying to get it done a little faster isn’t going to matter in the long run.