Take Isengard as an example. We will wish for it to work those 5 resource tiles throughout, and are probably not interested in whipping any unit for less than two population per cycle. The 6th and 7th population take 32 and 34 food to grow, with 15 and 16 saved by the granary, so 35 food to grow back from 60 base hammers whipped. A smaller city like Culture Bridge whipping from size 4 to 2 requires only 26 and 28 food, less 13 and 14 from the granary, so 27 food required for 60 hammers. The ratio cannot be anything like 3 hammers for a food.
I agree that the raw ratio is 2 to 1, however as you say later the organized and forge bonus changes this.
An earlier forge does give access to the 25% forge bonus faster. So there is a window when Slavery outperforms Caste when slavery has a forge and Caste does not, if the city has a meaningful hammer output during that time. Isengard, Gems, Stone and Washington would/could have such a hammer output. Other cities won't.
The earlier forge still helps the other cities with whips, so we need at least 6 cities, the cities were we plan to build universities or whip multiple military units out
Organized religion helps with the first few missionaries not needing a monastery. Then it helps in cities that have had the religion spread that are still building a building. The missionary cost 40 hammers to build, so we must build around 160 hammers worth of buildings in each city to which we spread, in order to get value for those hammers. A forge or university are respectively 120 and 100 hammers (considering that we are Philosophical and get half-price universities). Given that any strategy will need missionaries for GPfarm and Washington for the eventual
benefits, those missionaries are accepted costs. However, a strategy that spreads Taoism further in the short term has to consider the opportunity cost of building those missionaries. Those could be other useful units. Also, the forges might get built before Taoism spreads, which might make it hard to show a profit.
You prove my point. Any city we expect to build a forge and university will pay for the missionary in the hammer savings under organized religion. If we don't go to war what is more important than getting forges and universities in our key cities?
We don't need to convert them unless we think we need the shared-religion diplo bonus for the victory vote, and don't think successive espionage conversions late in the game will do the job. Religious shared-war could well be a better approach. The AP votes are binding whether or not you have adopted the state religion. Dominating the AP vote against pairs of AIs is easier if we're the only civ using the religion - but we'll probably be on top regardless.
Mass converting an AI to the AP religion has a lot of benefits. We can get them to friendly and trade monopoly techs with them for example. And I have proven that you can convert an AI using successive espionage. Plus if you convert the AI to another religion using espionage, it will not (in my experience in a recent 10-game challenge game) switch away even with a small number of cities in that religion if it is at war.
Also, the first city conversion from the first whipped missionary could be about 4 non-anarchy turns from now, and many of our converted cities will be substantially later than that. Monasteries cost 60 hammers, so we do want 20+ post-AP pre-Scientific Method turns of 2 hammers and 2 beakers to show a profit.
We need some monasteries, no not all cities will build them but the benefits are very close to matching their cost. Especially in cities that will produce significant research (by running multiple specialists during the caste phase of the game)
With a cap of three missionaries on the whole map, we are not going to be able to mass-convert anybody for a long long time. We're talking serious galleon chains here... Late-game Universal Suffrage rush-buying from hub cities might be the only way to do this fast enough...
I just played a challenge #1 game and I mass converted 4 AI on an oasis map before the UN was built.
Your calculations are assuming a forge, which only about half our cities will actually have. A 40-hammers monastery seems likely to be a single-population 45-hammers whip with a forge and OR acting together.
Monasteries are 60 hammers
Courthouses are a long way away. We have lighthouses in most cities, forges, monasteries and missionaries to build, more scouts, perhaps replacement spies, and sooner or later universities. I agree that courthouses are nice, but so are lots of other things we want to be doing.
Courthouses do not have to be a long way off! If we don't go to war then we definitely want to whip courthouses.
A grassland workshop under caste with Guilds returns 3 hammers per food. Assuming we're working several of them per city so that forge rounding effects can be more or less ignored, that's 3.75 hammers per food - or 108.75 hammers for 29 food. If we're not building a building (e.g. all those missionaries, spies and army we might be building), Caste still returns at this rate, whereas whipping reverts to 74 hammers.
One hidden cost is needing to wait until the AIs tech Guilds for us to steal. Before then, Caste workshops are not great.
Cottages are more than half complete. Plantations are underway. We're going to be looking for jobs to do if we
don't build workshops...
Sure build workshops, but without a switch soon to caste system there is no urgency to build them. If we do switch to caste system without significant whips then we will out grow our workers' ability to build the workshops. So the hammer production of those cities will be limited. Plus if we are in caste system it will be hard to justify working a workshop when instead we could run a specialist. So maybe you are right that we could build workshops for the few key cities that we don't plan to run specialists. But still the whips produce the buildings faster. And this frees the workers up to helping improve more cities...
That sounds like a gamble. This is a race we're in here... We're still in the dark about what tech we need to kill the wizard, but the sooner we get cranking the better...
per 
once a granary is up. With Caste, a grassland workshop returns 2
