I'm not an expert at BLM but I can offer you some advice that has worked well.
With large groups (like, for example, with speedrunning dungeons), it is a far better use of your time to throw off one Fire 3 (to get 3x astral stacks), then use Fire 2 until you are almost out of mana, and finish with a Flare. Don't bother with thunder -- waste of time on huge pulls. Then, convert+swiftcast for a second flare if needed. Keep in mind that this is the HIGHEST damage potential and unless a tank is really confident in his/her ability to keep threat, you may pull hate. Before 50, it may be a real problem, so be careful with this knowledge and watch your threat. I like to pop off raging strikes and quelling strikes before the first flare, just to be safe. After the second flare, you can transpose, throw off another Fire 3 to get your 3x stacks back, then a few Fire 2s and another Flare. Since you don't have Flare yet, you may wish to use a few Fire 2s, and then switch to single-target if you get close to pulling threat on anything but the 'main target' (tank should be marking).
While in 3x astral stacks, you can use Blizzard 3 to put yourself at 3x umbral. The reason this is preferably is because... it costs little MP while you are in astral 3x, no time is wasted, and Blizzard 3 will take far less time to cast while you are in 3x astral than if you had just transposed to umbral 1x. It's not a huuuuuge dps loss to do it the way you mentioned, but it is far more efficient this way. At 50, you'll want to use your last Fire 1 when you have around 1k mp (leaving you near 400 left), throw off any Fire 3 proc if you have one, then Blizzard 3 followed by a variant of thunder. If you planned correctly, there will be ZERO downtime 'waiting'. At 50, you'll be using this method to swap between having very little mana and having full mana quite often.
Keep in mind that BLM, for the most part, must be 'standing still' to do damage. Needing to move/dodge is a dps loss on its own, so try to alleviate this problem by throwing off your procs while you need to dodge if you have them... because otherwise you wouldn't be dealing any damage whatsoever. Plus, using procs forces you to wait on the global cooldown for your next spell anyway, so using them while you would be moving anyway is the most efficient use of them. I'm not saying let them fall off if you don't find a good opportunity to use them -- but rather, observe your surroundings and plan accordingly.