Honestly the differences aren't relevant enough for you to play something you don't enjoy, so my recommendation is to pick whatever spec you like (except fire being mandatory on fights like Tectus, because let's be reasonable here, Living Bomb OP
)
As for your DPS, you can definitely improve in that department, but you're aware of that which is good. Personally, I'm at 669 ilvl and regularly do ~30k on Butcher and Kargath, sometimes more sometimes less. This is close to my simulated values minus ~4%, which accounts for the many mistakes I usually make in a raid environment, so I tend to trust Simcraft completely on stand-still fights. The people behind the mage APL are remarkably knowledgeable about the class and they've done a fantastic job on simcraft as a tool.
I simmed your armory and you should definitely be doing ~28k at least (with a sim value of ~30.5k), and I can see from your logs that you're munching a lot of procs. In the Butcher fight, you synced MI and IV which wasn't necessary since you could've gotten a whole extra use out of it (syncing is necessary on Mythic where the enrage is 4 minutes).
TL;DR: Fire won't overtake Frost for single target anytime soon. Even when it does, it won't be by a lot. Arcane already is better for you on ST, but limits your mobility. Both will be better for progression in BRF than Frost (if the common wisdom in the mage community is correct).
Hope this helps