Order v Empyrean: No real reason to stick with Order from my perspective. It's just a habit from pre-Empyrean play. The main advantage would be the free Disciple units when the cities convert but without Spiritual trait and Spiritual Hammer, that's less appealing.
Spiritual Hammer: Hmm... I missed that. I only played on RoK game since that was changed and I used Arcane units for my beef on that one. In any case, Monks are still S6, require no resources, and are relatively quick with respect to the beakers needed to make them available, making them a decent rush option.
I have to admit, though, in light of the changes, I'm struggling to see a powerful Elohim-specific synergy.
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Priests: +1 Food is a bad, bad idea. There would never be a reason to run any other specialist, barring trying to manipulate your GP output. Even then, Prophets are among the most useful - good settlement option, Shrines, Altar. Unlimited priests in a GP farm at 1 food each would be insane.
Unless Fend for Themselves changed the food req, any cities could go entirely food-free (1 food to maintain the pop/priest, +1 food from priest = 0 net). Keep a few pop working the most profitable food tiles to grow the city to the happiness cap and then run them all as priests. Stockpile Prophets, then switch to another religion and sweep the Altar construction to win.
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Edit: Okay, I tested several game starts (Emperor, normal speed, standard size, shuffle, No AI Building Reqs) and I have to admit that without access to Spiritual Hammer it is very hard to get the Priesthood beeline to do much.