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More importantly, as Avenger if you wish to focus on fire damage, Ichaival provides highest base damage. None of said MI can provide such high base fire damage, so affixes do not matter as none of them can do more damage than Ichaival.
I chanced upon it when running over for another little dance with Toxeus with another char - Made me roll my first Avenger.... ...and I do ofc concede and know that I was pretty darn lucky there.
And re. lower resistances: Bramblewood does a fixed number, not a percentage reduction. Same for Flush Out, hence those stack nicely. 3 sec duration, 25% chance, and an attack speed well north of 150% makes the effect somewhat permanent, statistically.... ...and it's twice as high as Doomfang's is. And DoTs (and thus AFAIK / presumably also debuffs over time) do not stack in TQ, they just reapply and refresh their duration.
*shrug*
TL;DR: Bramblewood is annoyingly tough to farm, but if you happen to get a nice one, it's pretty awesome.
And since you mentioned such rare affixes on a rare MI, you should compare with enchanted Ichaival instead of vanilla one, which still does more damage than your bramblewood without RR proc. of the Betrayer, for example, which makes Ichaival also has chance to RR.
And for Tinkerer's affix and Doomfang Striker, in 2.9 you can't use two Incarnation of Prometheus' Flame, but you can use one Incarnation of Anubis' Wrath which adds more attack speed and more importantly ATDTH. You said you pick Incarnation of Prometheus' Flame on the bow, which means you will need to use artifact or amulet to find ATDTH. With Tinkerer's affix you are free of that and you can find other stats on these slots. Also RR is diminishing returns, you are not comparing with 50 RR and 22 RR, instead you are comparing 22+54 and 50+54, and the latter one is chance to proc while the previous one is always proc. I don't even want to mention that Doomfang has a fixed mini boss to farm with very high drop chance which Bramblewood does not.