First of all (and this is so important that I am kicking myself for not doing it during my turns) go to the governor and
turn on emphasize production. Set this as default for all cities.
BG = bonus grassland
Do not switch the Warrior in DC, and I'll tell you why as well as in great elaboration.
Currently DC has 4 food left until growth and 8 shields in its production box. It pulls in 7fpt and 4spt.
If you switch to a settler immediately, you can track DC's production and growth as follows:
Turn | Food | Shields
0 | 16 | 8
1 | 19 | 12
2 | 20 | 18 -- New citizen from the pop growth will work forest tile for +6 shields only for certain if we have emphasize production turned on.
3 | 13 | 23 -- New citizen switched from forest to plains (currently being irrigated)
4 | 16 | 28
5 | 19 | 33
Which drops our pop down to 1 for a turn and wastes 3 shields. Granted, after the pop change you can keep the citizen on the forest tile and get the settler out a turn earlier with no wasted shields. But you now have two turns that DC is at pop 1.
If you keep DC on the warrior and then build a settler, you get this:
Turn | Food | Shields
0 | 16 | 8
1 | 19 | 10 -- MM DC citizen off of mined BG and onto roaded flood plain to pick up additional commerce. Warrior completes IT.
2 | 20 | 6 -- New citizen from the pop growth will work forest tile for +6 shields only for certain if we have emphasize production turned on.
3 | 12 | 12 -- Keep new citizen on forest tile for first two turns (explained later)
4 | 14 | 18
5 | 17 | 23 -- Switch DC citizen working forest onto the irrigated plains.
6 | 20 | 30 -- On growth, new citizen will work forest for +7 shields this turn.
Now, by keeping the warrior first we have several important differences. First of all, DC never hits size one. I don't think DC should ever hit size one pop if we can help it. If we had a luxury around I'd say it should never hit size two, 2 luxuries then size 3 and so on. The idea is to keep DC at the highest population possible while it pumps out settlers so we pull in the most amount of commerce and production while the settler factory is running. Secondly, there is no shield waste at all. Third, we get an extra warrior out for MP duty / exploring / barb defense at a cost of only 1 turn. It takes a little MM to do, but it is definitely the best course of action IMO.
We can and should set up DC as an 8-turn settler factory by keeping this pattern:
Turn | Food | Pop |Shields
0 | 10 | 2 | 0
1 | 13 | 2 | 4
2 | 16 | 2 | 8
3 | 19 | 2 | 10 -- warrior completes
4 | 20 | 3 | 6
5 | 12 | 3 | 12
6 | 14 | 3 | 18
7 | 17 | 3 | 23
8 | 20 | 4 | 30 -- settler completes
As you can see, DC is currently on turn 2 of this pattern. Please do not de-rail it as it is our quickest way of efficiently getting settlers out.