You have fundamentals of BLM down just fine.
Important things to note:
Ice III - grants full Umbral Ice three stacks without needing to Transpose
Fire III - grants full Astral Fire three stacks without needing to Transpose
It takes two clock ticks under UI3 to regenerate full MP. This usually gives you enough time to cast 1 Thunder spell (use the highest you have MP for).
The clock ticks every 3 seconds but you could enter the UI3 state very short before a tick, thus, your two clock ticks could be as short as 3.5 seconds or the full 6 seconds.
It takes about 2 seconds to cast Fire III, thus, you can learn the timing such that you start the cast and it finishes like 1/2 second after the UI3 clock tick at full MP.

Now, do not get rid of transpose, you still need it, when using Flare or you slightly mess up the MP management and cannot afford to case Ice III.

To Flare or not to Flare. I generally follow the rule, 4 or more enemies, go full AoE attacks.
F3 > F2 > F2 > F2 > Flare > Convert > Flare > X-Ether > Swiftcast + Flare > Transpose > Thuder > F3 (start over)
There might be room for another F2 but I cannot remember for sure.
Note: above level 52, the third Flare is no longer possible without using lv60 potion.

Single target:
T2 > Swiftcast + F3 > F1 > F1 > F1 > F1 > I3 > T? > (dending on clock tick/fire starter proc possible Scath) > F3

Hit all Fire starter procs, except ones the proc on the last F1, save that for transition back to AF3.
Hit the first Thunder Cloud (TC) proc under AF3. If you get more than 1, just save the second until UI3. Hit all TC procs under UI?.