I doubt a Theology Sling is possible with the Oracle on Emperor without forgoing some very important worker techs.
I favor no early religion, especially at the higher levels. I think its important to give the AIs every excuse possible to be at each others throats, and religion is one of the best. My vote is a Priest economy with our UB, and bulb Theology, and push for the AP, switching to a religion none of your neighbors have before its done (but one thats in the city building it). By then, you should have enough of a defensive set-up leveraging the PROT trait to ignore any negative diplomacy because of religious differences. Take whats around early when it spreads to maintain peace, but plan to shove it in their faces with the AP, and rack up some GGs when they suicide on your Walled LBs.
I love the Priest based SE. Its even very doable without the Mids, and you certainly dont need an early religion, in fact, as a few have already pointed out, taking one is likely to create an "AI Block" of the other. IF you go for an early religion, my advice is to get them both, and since I dont see a 3C tile, thats probably not very likely.
I had a game in the LHC, was only Monarch, but I got Hinduism. By the time I met the other AIs, I was in trouble because they were all Buddhists, and the ones who werent had been vassalized by the ones who were, which is even WORSE than just being "friendly". I replayed that game, and actually managed to get all 7 religions on Monarch, but I knew I was isolated, and India has much better starting techs than Arabia so it wasnt nearly as punishing. I also replayed it by not bothering with a religion until Confu, and that turned out to be the best of the 3, because the other AIs got Buddhism, Hinduism, and Judaism, and fought, a LOT, so there was minimal tech sharing, minimal friendliness, etc etc. Ever since, I have totally avoided either of the 3 early religions, period. Let the AIs have their Holy Wars, and be ready to pick up the pieces and hope for them to pop their own Prophets and build shrines for you until your ready to pounce.