I've been playing with ACKS' domain growth math recently. The random +1d10-1d10 families per month cancels out in expectation. The adventuring bonus is only 1% per month for domains of any reasonable size, which helps but won't take you from wilderness to civilization in your lifetime (12.7% per year will take you 10 years of adventuring every month to bring a freshly-secured 24-mile hex of cleared wilderness domain up to borderlands, and another 15 years to population-capped civilized). The only other ways to increase population are investment, at the rate of 5.5 families on average per kilogoldpiece invested, and high morale, yielding potentially another 2.2% average growth per month.
A family in an average domain generates 12 gp/mo of gross revenue, and has expenses costing 7gp/mo. A new ruler could drop taxes to 0 (+2 to morale rolls) and hire an extra 3gp/mo/family of garrison (+3 to morale rolls) without taking a monthly net loss. With +5 to morale rolls, every season there is a 1/12 chance of dropping towards apathetic, a 1/3 chance of gaining one level of morale, and a 7/12 chance of gaining two levels of morale (in expectation, +1.4 levels of morale per season; better if you have a positive Charisma modifier). This should converge to Stalwart (maximum) morale in 2-3 seasons, at which point income per family rises to 14 gp/mo gross, and you also get a growth bonus of 2.2% per month. Combined with the adventuring bonus, this would yield ~3% growth per month, which would allow wilderness to borderlands in about three and a half years with no costs to the domainholder besides building and maintaining the castle.
Similar results could be achieved by sinking all of one's domain income back into agricultural investments; at 5gp net per family, every 200 families yields 1000gp/mo, or another 5.5 families per month, for a 2.75% monthly growth rate. This does leave one without the secondary benefits of a happy populace and the strong garrison that the morale approach provides. It also suggests an improvement to the morale approach; if we sink the 2gp/family/mo from being Stalwart back into agricultural investment, can get another 5.5 families per five hundred (+1.1%/mo), additive with the Stalwart bonus, for a 3.3% monthly growth rate; with active adventuring, this is 4.3% per month.
Of course, any growth rate above 5% per season also provides us with a +2 bonus to morale rolls. 5% per season is only 1.63% per month, which should be achievable by any of these means. The extra 2gp/mo you can then extract in taxes while maintaining stable Stalwart morale yield another 1.1%/mo growth via investment (additive with other morale and investment increases), for 5.4%/month growth with active adventuring.
(Also, if you have access to ritual magic and >125 families total in your domain, Harvest is a net win. When cast on larger domains and reinvested, it approximates +1.1% growth per month for a year.)
Even with that sort of all-in reinvestment strategy (ignoring Harvest), growth from wilderness to borderlands takes 24 months. Growth from borderlands to civilized takes another 13 months, and then civilized to capped-out civilized takes 19 months. Meanwhile, during the first fiveish years of your rulership, you have effectively extracted a princely sum of 0 GP from your domain! (Less if you count the cost of your fortress and its maintenance, though you might've earned some XP for money that you reinvested in agriculture and voluntary overgarrison, depending on your level and your DM) On the plus side, you're way over-garrisoned (which is to say, secure), the peasants love you, and after the population has capped out you can raise taxes and drop the garrison, at which point your lands will yield 62000 GP/mo, which is above the domain XP threshold for all but 13th and 14th level characters.
I've ignored urban centers here, because their gross per family is much lower than rural peasants (7gp/mo/family vs 12) with similar monthly costs per family. They're basically money-sinks. You want one for a market, but expect to pay for it out of adventuring revenues, because it will not be both growing and profitable, and possibly neither. Note that I have ignored hijinks here, because hijinks are hax in their current form. I guess I haven't done the math on granting yourself local monopolies on all goods either; it looks like you can make on average a 20% spread on arbitrary goods by buying them in your town with the monopoly bonus, then selling them without moving them a month later ("Hello, I'm John and I have a system abuse problem."), or 40% spread with bargaining, but it would take some seed money and is very limited by the number of merchants available. It could add up over time, but I don't think it would be even remotely near enough to feedback into urban growth.
The obvious problem with the Land of Tax-Free Prosperity approach is that most campaigns do not last five years of game-time (plus time spent clearing or otherwise acquiring the domain in the first place). Even if you slow the rate of adventuring down to the adventure per month needed to keep your growth rate up, sixty adventures is minimally 30 sessions is most of a year of weekly games. Hell, the two years from wilderness to borderlands are liable to take the entire lifespan of an average college campaign. We hardly made it through a a game-year in six months of playing weekly (and sometimes more often than that).
At the end of the day, offscreen time is cheap in terms of realtime, and adventuring time is very expensive. It seems to me that if you actually want to see really substantial domain growth in the time it takes to play a campaign, you need to hold down the fast-forward button a bit. With full reinvestment in a Stalwart domain, you can make it from Wilderness to capped Civilized in 6 years without adventuring rather than 5 while adventuring monthly. This sounds a lot more doable, and gives the PCs time to relax with their feet on their desks, do some spell research (though with funds limited by infrequent adventuring), start raising a family and some heirs, soak up some domain XP, and maybe earn some aging penalties between annual or biannual adventures in the Pendragon model. Gives you a nice sort of interbellum Golden Age between the bloody business of clearing the hexes and dealing with domain-level crises like the Mongol Horde or the succession war following the death of the Wise Old King to whom you swore fealty or suchlike.
Another way to do this might be to place seasonal restrictions on things. Adventuring and war are strictly summer activities; mercantile activity is resolved with the autumn harvest, the winter is spent intriguing in court, and the spring is for tournaments and weddings. Rather foreign to our modern sensibilities, but might make for a useful game framework for domain play. At some point, things are stable-ish, your reign is secure, and it makes sense for the pace to drop.
I suppose the other option is to continue adventuring at the normal rate and assume that almost all growth comes from adventuring revenues invested in agriculture. This is... a subject for next post, because this is already long.