In this example, me too. Brawling is the skill for applying your Power to someone to subdue or wrestle them in a skilled manner. I wouldn’t separate out Brawling and Power in an example like this*
In this example, where the roll has happened, if I really wanted the Cultist to escape (or have a good chance to escape) and you’d succeeded on the stated Intent. I think we’re agreeing loudly mostly, but it’s Christmas and I feel like agreeing loudly about Burning Wheel.
Then I likely would try and claim that the situation had meaningfully changed when the ritual completed. I would draw attention to the clear differences in the scene before and afterwards, and the clear difference in the Intent of the NPC, and in fact your Intent, now that the Ritual has changed the world. I imagine you’d lobby for your Intent and Task being sacrosanct according to Let It Ride, and I’d either agree, introduce a new complication to the scene so it looks even more like LiR can stop applying, or reach a different compromise; I’d expect you to lobby for Advantage for having subdued him already.
*If I really really wanted him to have a chance to escape and to separate Brawling and Power, then I’d narrate a dark portal opening up where the cultist is and him being sucked through bodily by an immense magical strength. That’d be a Power test with LiR definitely not applying, after a Brawling test, with a very similar Intent and Task overlap.