I've recently put together an updated version of Fractal-Hope that has largely allowed me to EM Fire Queen reliably. The version I was using:
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5j2 5j2 5j2 5lk 5lk 5lk 5lk 5lj 5lj 61o 61o 61o 61o 61o 61o 7hi 7jp 7jp 7jp 7jp 7jp 7jp 7k2 7k2 808 808 80i 80i 80i 80i 8pp
Base requirements are 6 RoLs, 3 shards, and 1 Miracle, but it's pretty much a guaranteed EM against Fire Queen unless you get a really bad draw. She always focuses Snipes on the highest damage RoLs from what I can tell, so you can build up your RoLs safely.
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5j2 5j2 5j2 5li 5li 5lj 5lk 5lk 5lk 5lk 61o 61o 61o 61o 61o 61o 61o 61o 61o 61o 622 622 622 622 7jp 7jp 7jp 7jp 7jp 7jp 8pp
This would probably be the base minimum, though 2 miracles offer better coverage.
You could also conceivably throw in a dessication or two, and replace the sanctuaries with purifies if you feel the need (sanctuary is only there for EM, so purify works as well). Water quanta is fairly free once you put down the first shard. There's decent room to play around with it.