Sorry for my absence lately. Work has been crazy. Also, I'll be out this weekend with limited access to Civ. I'll try to keep up with what's going on, but my
useful comments will likely be minimal.
Regarding the plan:
Rheims: I'd like to take this city as soon as possible. Swords, cats, maces, I don't care. With our current army of axes, chariots and a sword (maybe one more), we should be able to take it without much issue. We may even capture another worker or two while we get our army in position...

Once we own Rheims and have the stone quarried, I'd love a chance at the Hanging Gardens in Moscow (~4 turns to build) if they are still unbuilt. Not likely, but possible.
That stack of city defenders in Marseilles looks a bit daunting (3 archers, 3 spears and 2 axes). Luckily they are cut off from Rheims due to our road pillaging.
Theocracy: Swithing to Theocracy only seems worth it if we plan to push our advantage with maces and cats all the way through Mao (ala bcool). If we are planning to take a few French cities and then stop, then I'm not sure it's worth it to be out of OR for too long (plus the extra turn of anarchy to get out of Theo).
Hagia Sophia: I still think we should build this wonder. I don't think that the worker efficiency is just a side benefit with the GE points being the major benefit. We have a TON of worker turns ahead of us. More efficient workers will help us set up cities that much faster. We can also get started on sending a worker or two up north to start roading and scrubbing in preparation for Operation Iceball.
Iron Works: I don't think we should put it in Moscow even though I brought it up earlier myself. There will be a ton of good options to build it when the time comes. With full-powered workshops, Sid's Sushi and Mining Inc, just about any city with a lot of land tiles can be a hammer powerhouse. I played a space game recently using a Hammer Economy (SE early game and HE mid-to-late game) combined with Mining Inc (no Sid's due to lack of rice and seafood) and I had 10+ cities with 50+ base hammers. Every space part could be built in 6 turns or less and I had 10+ cities to handle the load. I had never really played a HE before (not fully understanding the power of the workshop) and it was very flexible. I could easily switch from building wealth, wonders, units or space parts. I got DOWed in the late game and was able to spit out a modern armor from 10+ cities every one or two turns. I kept the research slider at 100% for the last 100+ turns in the game because I could build wealth in a city or two to keep it going. In our game, we have way more Mining Inc resources (I had 12 IIRC) and Sid's will allow us to build more workshops and fewer farms, making it very probable that we'll have 10+ cities with 90+ base hammers.
BTW, the cost of Mining Inc was negative in my game (a negative cost = a profit...

). I had Wall Street in my Mining Inc headquarters. Every time I spread my corporation to a new city, my expenses actually went down because the income in my Wall Street city more than offset the corporation cost in each new city. My HE could produce an executive in 1 turn in most cities, so spreading Mining Inc was very fast and very effective. I think Mining Inc and Sid's Sushi are definitely the way to go in this game.
Regarding advancing the game, Dhoomstriker was adamant about always leaving at least one unit active before uploading the game. He would wake up a city garrison if he had to. That way, a simple accidental press of the space bar would not advance the game but simply skip that unit's turn. Something to consider, although in this case, the impact was nearly zero as it seems we were leaning toward building a sword or three in Moscow anyway.
Edit: x-post with BBP.