I'd almost dare say the STR bonus is what effects the damage with atmas. Which would be consistent with how merits and crimson howl and gear never seem to make that much a difference in the attack department.
I most definitely agree that the STR bonus is going to make a big difference in the damage, especially since there is such a huge multiplier. I think the big thing to consider here, though, is that avatars cap out around 4.0 pdif, whereas a lot of players cap out much lower (ie 2.0 pdif for one handed weapons). Thus, it takes a hell of a lot more attack to cap out your pdiff on summoner than it does on a melee job, and you have access to FAR less options than a melee job does. As you are well aware, the highest damage of bloodpacts is on squishier stuff where you have a capped or closer to capped pdif, and the same can be seen with their basic melee hits too.
Thinking about it.... +15 attack on royal redingote, +15 attack from merits, +50 attack from stout arm (potentially +70 if they also gain 20 attack from 40 str, but we are unsure of that) is +80 attack. Can add in things like karura hachigane if garuda, and the relic feet add a bit of attack (keg testing showing that it's really not that much unfortunately). Also, the fay crozier or better yet, the fire magian staff with pet attack on it. Crimson howl is a little limited compared to things like beserk, minuet, etc, being less than 9% of a boost. Crimson howl boosts 400 attack by just under 36, and berserk by 100 respectively.
But considering 80 attack... a melee, if their attack is high enough, gets 85 attack from using a yellow curry bun alone (in a party of 4 or more...) and a little bit of strength. Add in to that things like Amemet mantle/Foragers, Jewelry with attack (like aesir ear), ammo like bomb core/fire bomblet, etc and they have a LOT more attack that they can strap on. Also add into it chaos roll, and minuet... because no one is probably going to use Beast Roll for our avatar. The amount of attack that they can strap on is enormous compared to the limited resources summoner has.
Also... I have yet to confirm if cruor buffs work on pets yet. I'll have to run in as 37 pup and get buffs, and see if they add to my automaton as well. If they add to my precious Koumei, I'm sure they will add to my precious Shiva and Garuda as well. But if they don't work on pets, that's another attack bonus that melee will have over our avatars...
But yeah... I think all three of the factors work to increase the damage a lot. I think STR pushes the potential damage way higher (obvious), critical hits from razed ruin not only have a greater impact because critical hits are enhanced further, critical hits serve to increase pdif. Attack will greatly increase the damage by raising pdif.
But considering that two decent +str atmas (eve and briareus) likely DOUBLE the base strength of the avatar, that's pretty huge.
Upping the critical hit rate by a huge amount, and increased the damage done, is going to boost up pdif a lot.
Giving an Avatar +150 attack, which you can't even get that much from atmas (and would need some gear), isn't even going to double the attack that they have when compared to strength. Going strictly for attack will yield the poorest results because you aren't getting the most "bang for your buck" persay.
So yeah... you have it right. STR and critical hit are the best you can likely use physical bloodpacts. I don't think though that the problem with attack is that it doesn't do too much. I think the problem is that we just don't have enough access to it for it to truly be as successful as it is for melee jobs. I would love to see pet that we eat be used by our pets, similar to atma, but the problem there imo lies in balance. Giving an avatar a big attack boost probably wouldn't be game breaking, but giving it to beastmaster or puppetmaster may be, considering they as the master have much more use than we do for something like yellow curry.
And as a side note... I've always enjoyed your summoner passion, Mellowy