Oh, dude. A little knowledge is a dangerous thing.
Certain bacteria will, indeed, decompose cyanuric acid under anaerobic conditions; I don’t think you want to encourage that sort of thing in your pool.
There is a chemical pathway to degrading CYA; it’s normally regarded as a problem, so it’s unlikely to have been studied as a deliberate technique; it requires higher temperatures, so it’s unlikely to occur in the winter; and it would take years to lower your CYA levels significantly.
It would take many, many gallons of mineral oil to create a stable boundary layer on the surface of a swimming pool, and you’d have to drain to get rid of it. As you’ve discovered, water excludes oil by minimizing the size of the boundary, which gets you huge blobs, not a thin film.
Detergent will not make oil spread out across the surface of the pool, it will solubilize or sequester it, depending on the ratios involved. A significant part of your pool is now, essentially, skin lotion. Cheap, nasty skin lotion (or - depending on how much detergent you added - cheap, nasty conditioning shampoo).
All you’ve done is contaminate your pool, and I can’t begin to guess how it’s going to affect your filters and whatnot. Yeah, draining. More than if you’d just left it be, I expect. Though I respect your determination to avoid wasting water (California? Me too), you and the environment would have been better off if you had, say, come here first.
Moral: Tri-Chlor tabs are bad, m’kay?