Second Derivative Theory:
Uriel didn't give Harry Soulfire
It is my theory that if my above "Foundation Theory, and First Derivative Theory are true, then when Uriel “jostled Harry’s elbow”^xrt#3 he did not invest part of his own energy into Harry to give him access, but rather nudged Harry into pulling the trigger on the Soulfire gun that was already in his hand, and made available to him through his latent connection with Lash who had already used Soulfire.  This would make Uriel’s “favor” a truly small one, and reinforces the Foundational Theory.  (props to LML for the trigger/gun analogy)

Lash might have used some of it to help Harry out in defiance of her coin's purpose, but I think Harry first tapped soulfire, somehow, way back in book 2.   I was rereading Fool Moon a while back, and this passage jumped out at me:

Somewhere, in all of that, I touched on something that wasn’t tapped out, in spite of how horrible the past days had been, something that hadn’t gone cold and numb inside of me. I grasped it, held it in my hand like a firefly, and willed its energy out, into the circle I had created with the spinning amulet on the end of its chain. It began to glow, azure-blue like a candle flame.  The light spread down the chain and to the amulet, and when it reached it the light became incandescent, the pentacle a brilliant light at the end of the chain..."  Kindle location 4354

It isn't the amulet itself that is glowing blue at first - it is the energy that Harry summons from inside himself.   And the blue light amplified the power he was pumping into the amulet already.  That seems like a soulfire boost to me.  I don't know how angelic beings figure into it at this point.  But Harry guesses later that the Black Council was behind the wolf belts - perhaps they were "cheating" in doing so, which in turn allowed for somebody to give Harry a little boost.

Edit to add: Related to the thought about cheating, when Harry soulgazed Denton, he saw the agent's formerly orderly self coated in "a thick, sticky black sludge that smells like swamps and things that attract dun-colored flies" (Kindle location 3955).   At this point in the series, that makes me think of the Formor.  And they seem to be bad guys, or at least have bad things in mind for Chicago magic users.