The Sound of Music must be your favorite Lovecraftian movie, then (I mean, I assume you didn't realize it was Lovecraftian until I just pointed it out. Certainly, there are scenes in that movie that invoke unmentionable dread.)
One does not simply run out of occupied Austria...
I guess I don't get the point of applying the label "Lovecraftian" if the only thing that it borrows from Lovecraft is the notion that big bag monsters may be hard to physically describe. The writing style is not Lovecraftian, the themes are not Lovecraftian except in a very general sense, the narrator's voice is not Lovecraftian. The concept of a warding circle is definitely not Lovecraftian. The idea that anyone could control or bargain with the supernatural is arguably present in some of Lovecraft's work, but never in as direct a form as here.
I mean, taking this story to be a response to some of the problematic aspects of Lovecraft, certainly. But I don't think this response shares enough with what it is responding to to be called "Lovecraftian".
Logistically, we rarely see the cultists point of view in Lovecraft's own work, and the protagonists are too busy running away (or going mad) to let us see the deals each makes. But deals
are made, with varying levels of efficacy and cost for the cultists. That said, I think Sarah overstates her own role in "pointing it toward Atlanta" and how much the critter really has in common with her. You are right that it doesn't share a lot of the Lovecraftian trappings (besides the big critter). But I think there's something Lovecraftian in the theme.
The key, defining bit of the Mythos for me is the existential dread - that all of humanity is unimportant and ultimately doesn't freaking matter to the bigger forces out there. That there is no bigger "meaning" or purpose - that it's all futile in the end. The big critters are just window dressing to illustrate that point.
With that idea in mind, Sarah's actions - and those of Sherman, and those of every slaveowner, of every person who does evil things in the name of what they view as "good" - become even
more horrific. When the only meaning in the universe is the one we give it... well, that makes every act of cruelty all the worse.
Because, if the Mythos is right and there's no purpose, and we're simply unimportant specks of matter, then nothing is justified. Our sacrifices and compromises never,
ever count.
And that really does horrify me.