Mythril ingots are goldsmithing anyway. Level 38 cap for 4 muthril beastcoins, 40 cap for 4 ores what level are you currently?
You could be failing so much and losing stuff for crafting on the wrong day so to speak- watersday - watersday is strong to firesday, you get more hqs (aparantly, it does work just never when i want) and a lot more breaks. I prefer fire and darksday for a fire synth, also i face NW when doing them (Dont know if directional crafting actually works, but i like to think it does anyway :D)
Unfortunately my mule is my crafting character, and also my desynth whore. As such my mog house is full of tarutaru stools for my overwhelming desynth energy. I find the energy does help though. You want as much as possible to limit the loss ive found. ( you still will lose some especially desynthing though.)
The fire enhancement does help for synths, it depends on how far below the cap you are too and what support your using still. I like this resource for all my crafting
http://ffxi.lokyst.net/timer/crafttimer.html
Basically, once you plug the synth cap and your level and crystal in, you want the numbers on the right to be between 1 and 4 generally (unless its real cheap then juyst spam away) This seems to give me best synth results anyway.
Back to your point on the energy though, it does help you lose not as much i believe, unfortunately bar desynthing - which can bne ultra random as it is - i havent experimented about with it enough. Try putting more in and maxing out the energy, theres 3 stages i believe - aglow with fire energy, aglow with powerfull fire energy, and aglow with overwhelming fire energy i think anyway. Ive read about elements helping crafters though, and know woodworkers who cange their entire MH depending on theyre synths.