I have yet to see the bug that cannot be beaten by going back and replaying the thing again. Since it is how you play that breaks the game, playing it differently usually avoids it. But you have to go back far enough before you triggered the bug. What triggered it could have occurred before the fight.
You have absolutely no idea what is going on and your assumptions on this bug are way off (no offense intended). It is not "how you(we) play" that breaks this as I have tried so many variants on this fight from fighting butt naked, to literally using a pickaxe for a good half hour, to combos of spells and shouts. I have no uber weapons, I am not killing him fast, I did nothing wild and crazy and even tried different diificulties. Playing up to the fight I tried several saves prior to even entering his domain. The issue here is no matter what you do (for those of us bugged)...when Mirrak is weakened enough to go ethereal and to the center, the dragon he sacrifices has it's soul go straight to you and not him. I even saved here and re-loaded that event around 10 times and every time I get the soul and Miraak stays standing there. Killing all the dragons before fighting him, taking 30 minutes to punch him into that state, running like a chump when he calls in his dragon to avoid being close...nothing works. I even jumped off the damn platform to avoid the soul and I was ported back up standing next to Miraak just in time for the game to "Dragon Soul Absorbed" me. He does not regenerate health in that state so waiting did not work. This is utterely game breaking for the dlc.
I reloaded a save prior to coming to Solsteim, I just wasted hours gorting back through the content but this time instead of exploring I just focused straight on the main quest. DLC was reinstalled and the end result was EXACTLY the same. Restarting the entire dlc may work for some but I wish I could get back the hours of my life I just wasted trying in vain. My last idea is I hear Miraak steals dragon souls when you are out normally fighting dragons. This has yet to happen to me and I am wondering if maybe that would trip him into actually being a friggin Dragonborn and taking a soul. I'll give it a last try and post back with results. This is one reason I prefer playing on the pc over the console as console commands could help debug or advance the damn quest past this bug.
If anyone has actually had the dragon soul glitch and fixed it please share it. I see trolls posting idiotic things to get people to waste time trying to trouble shoot this so I came here to the official forums as I know the crowd here is helpful and usually a lot more mature.