Mitchum said:
How valuable is early Construction in this scenario?
The answer, in my opinion, is that it depends upon the existence of at least one Strategic Resource, preferably Copper or Horse.
Catapults can't kill in BtS, so we need Axemen, Chariots, or Swordsmen to actually kill off the defending AI Archers.
One other possibility is to try and Oracle Feudalism. However, there are no Vassals allowed as per the game's settings, thus we might just end up speeding the AIs' path toward Longbowmen.
When it comes down to it, really early Longbowmen + Cats are decent, since the Longbowmen can go up the Drill line by winning easy battles early on and then continue to win battles later due to all ... but since we aren't Protective, we'd be stuck with Drill I and Drill II for our first promos, which are pretty terrible. Thus, I'd rather have Swordsmen than Longbowmen.
Self-teching Iron Working and Oracling Construction is cheaper than self-teching Construction and Oracling Feudalism... although the real value of Longbowmen would come in if we had ZERO Strategic Resources and were "walled in" by Peaks and Tokus.
Since we're likely to learn Animal Husbandry and Bronze Working before we build The Oracle, we can try and make a judgement call before building The Oracle based on which, if any, Strategic Resources are available to us.
It is likely that if we have zero Strategic Resources, a team that manages to take down Toku's Peak-surrounded City will do a lot better than the teams who don't do so.
Catapults and Archers won't cut it, so without Strategic Resources, Feudalism is something that we'd just have to bite the bullet and research.
I forget, but I think that you still need Writing in order to tech Feudalism, right?
Mitchum said:
How long will it take us to build/chop/whip an army of cats and chariots/axes large enough to take Kyoto?
Well, it will help if we skip building Granaries and skip building any more Libraries than just a single one (for a possible Math Lightbulb due to being Philosophical).
Pre-Chopping some Forests to go into Catapult builds would also be of use.
Generally, a good Catapult rush has us stopping REX when we have a Settler for our 4th City.
That way, you have time to grow your Cities and to possibly build a couple of Barracks.
Ideally, you'll be able to whip and Chop some Catapults (and/or other units) in your first 3 Cities and Chop some more in your 4th City.
So, our settling locations would be geared more toward the short term than the long term.
For example, we might settle an area with several Forests as a priority.
I still like Gold-1E and Pig-2E for their Resources and their Forests.
Marble by the Crab + Banana isn't very hot in terms of the number of Forests, but Marble on the Plains square by the Fish, which has some Forests, would require a Cultural Border expansion before we could even start working on the Marble.
We might not even want to settle a Marble City, but if we did, I'd probably say settle it to get the Fish + Marble if we manage to build Stonehenge, then be prepared to wait a while for our Marble to come online.
If we're going for an early Catapult rush, we won't care so much about Great Person pool pollution from the Great Prophet Wonders (Stonehenge and Oracle) all that much, as we'll be unlikely to spam a ton of Great Scientists and if we do, we can likely spam them from captured AI Cities a lot more easily than from our own Cities.
Of course, Forest Chops going into 2 Wonders means less Forests for Catapults, but so be it.
Stonehenge
I got to thinking about Stonehenge, and it WILL be valuable if we plan to go conquesting the AIs (for Domination or a Religious Victory). How come? Well, every initial AI City will start with a Religion and we're likely to see Buddhism being spread even further as a result. We're stuck in Hinduism, so we can't get Culture from Religions.
Normally, you eventually stop building Monuments because you can run Free Religion or No State Religion and count on the fact that captured Cities will have their Cultural Borders expand thanks to the precense of a Religion. Here, we can't count on that fact, so those Monuments actually become valuable mid-game, making them more useful than in an average game where you could just get that same Cultural expansion from running No State Religion without any extra effort.
The Deer + Gold location isn't particularly strong, anyway--it's decent but not top-of-the-line... the same could be said about the Marble location but at least the Marble location helps with expanding our Cultural Borders and gets us Marble.
I would be happy to wait on building the Deer + Gold location until after our initial rush captures us an AI City or two. Of course, Hammurabi could come in and settle the Gold in a poor location, or settle the Deer such that it misses the Gold, but if we're going to rush with Catapults, going for 5 Cities really starts to push things--it can probably be done thanks to us having Fast Workers (thus meaning that more Forest Chops than normal will be possible), but still, it's pushing it to go for 5 Cities before rushing and we should definitely not plan for a 6th City until much later.
Skipping the Deer + Gold location until later also lets us avoid Hunting for longer, too.
Mitchum said:
Should we make a run at the Pryamids?
Sure, but perhaps a half-hearted attempt, started only after we have successfully captured at least one AI capital.
If we get our war momentum going, we can always consider trying to capture The Pyramids should they get built elsewhere. If they can't be captured, then so be it--we'll just be using the base Hammers in units first instead of base Hammers going into The Pyramids and then using bonus Hammers from Police State to, over time, make up for the lack of units due to having spent our Hammers on The Pyramids.
I'm no longer convinced about going for intentional Failure Gold, since a Catapult rush is really Hammer-intensive. If we're going to be happy with pausing our REX at 4 Cities total (including our capital), then we won't really be incurring huge Maintenance Costs anyway.
Later, we can try for The Pyramids and optionally end up getting Failure Gold for it (not intentionally, but you take what you can get).
The real trick is not how many Cities we can have but how well we can set up whips and Forest growth at the time of learning Construction. A 5th or 6th City sounds good in theory but would be unlikely to repay the investment cost of the Settler unless we have a ton of excess Worker actions and Forests to Chop. Having those Gold and Gem Resources could throw off the balance a little bit.
Also, we don't have Fishing for Fish or Crab, nor do we have Calendar for Banana, so skipping a Marble City like ZPV seems to be suggesting could also be a viable approach--sure The Oracle would cost more without Marble but it will also cost us less to build The Oracle without Marble in the short run than to build another Settler for the Marble City.
So, a very viable option could be to settle the 2 Gold locations and the Gem location and then completely forget about the Marble location.
Obviously, a Horse or Copper Resource appearing somewhere could change things, but assuming that those Resources don't appear near Marble City, then Marble City is, admittedly, not going to be a very strong early City--but nor will the northern Gold location really be.
The Gem City location will be strong if we settle Pig-1E and give up on some production capability from Grassland Hills relative to settling Pig-2E, but I still wouldn't mind settling Pig-2E if we can complete Stonehenge somewhere.
I did pull off a nice Currency sling in 1200 BC though. 
Where do I sign?
per turn increased by 1 on 3000BC, consistent with having a 1cpt building starting on 4000BC. So that would be a monument or a castle...
