You are assuming that the REX will be economy-limited. I am assuming it will be land-limited. 6 AI. Small map. Mostly water. See what I mean?
The sea levels are low, and to compensate for being mostly water, I think Archipelago maps are larger than other maps. I only have anecdotal data for that, however.
Not in my tests. Only east-west.
Correct. North-south circumnavigation didn't work in my test, though I seem to remember a hub-spokes multiplayer human game where I did it with a north-south warrior. Don't quote me, though.
And while you are testing how to get the GLH, why don't you also test how many settlers/workers/galleys you can get for 200hammers. Just a thought.
settler+worker+galley = 210
Clearly that gives you a leg up on a second city to build defensive units while the food-rich capital keeps on with the settlers and workers. The relevant issues are
- whether the extra time gets you get extra cities from your main REX stream,
- whether you get any extra cities from a side REX stream that you establish earlier having avoided GLH, and
- whether you can pay for it when you're done.
It doesn't seem all that likely that you'll get another city with spare time to build a surplus settler if your civ has been successfully REXing defended cities with some workers scattered around before the available land is full. Thus it seems unlikely that the earlier REX start will amount to more than 1-2 cities difference when the land gets saturated. Obviously the amount of available land is critical here. If there's lots, then your second REX stream will give a boosted response. In my test game, land-filling wasn't going to happen until well after 1AD.
Please keep track for me of how many coins your GLH is actually netting you in 1000BC.
None
In the Contender test game I linked above, I built WB/WB/WB/warrior/worker/lighthouse/GLH completed in 1680BC (turn 58) simultaneously with finishing mining/sailing/BW/masonry/wheel/pottery/writing. I juggled around the warrior and worker so that I whipped the worker before finishing the warrior. By skipping the third WB you can get GLH a few turns earlier. One AI had contacted me, but apparently I wasn't eligible for a trade route (perhaps they need sailing too!). I got Alphabet in 875BC, and circumnavigated with a WB just before 1AD. An AI beat me to it by a handful of turns, because I experimented with a N-S circumnavigation.
By 1000BC (turn 75) I was still on one city (having built two explorer WBs while regrowing), so GLH was earning nothing.
By 500BC (turn 95) I had four cities. The
additional two trade routes were earning 6/5/2/4

respectively. I assumed the most profitable route in each city would still exist without GLH, of course.
By 1AD (turn 115) I had six cities and parity with the tech leaders. I acquired Currency somewhere in there. The two GLH additional trade routes earned 6

in each city, despite two of the cities having not yet built a building and only just having had their cows pastured. There were still three more Dike-worthy city sites that I knew were available. I'd recently popped my Great Merchant and was researching Machinery while holding Monarchy, Calendar, Currency and Compass. I was producing 96bpt at 80%.
Assuming a linear increase of GLH commerce between these two points (not quite valid, but it'll do for this discussion), we can integrate the

gained with the trapezoidal rule:
0.5*(17-0)*(95-75) + 0.5*(36-17)*(115-95) = 360

plus the GM.
That seems like a fine return for the first 57 turns of a 200

investment, with the recent trend due to continue for another 10-20 turns while I finish the REX, and a steady increase of a unknown slope due to come after that as the trade routes grow.
It would be really, really nice to get a settler out before the GrLightHouse. That will be my next series of tests.
That might be a useful comparison, along with straight REX. I'll do that on this same map over the weekend.