For one game, it was my strategy to have as many people as possible. However, I then reached a popuation limit, so I don't know how to make that a viable option.
No, you were on the right track. http://i123.photobucket.com/albums/o303/blueskirt_bucket/BestScoreEver.png
This is my highest score ever. After capturing a couple European colonists, burning some natives villages and finding some lost cities thanks to early Hernando de Soto and Cortes, I managed to quickly settle a nice money making industry as the Dutch with the help of Stuyvesant's custom houses.
Pro-tip #1 - The founding fathers offered to you are randomly selected I believe. When the game offers founding fathers you don't want or need right now, pressing the ESC key will close the window until the next turn, you can keep doing this until you are offered the founding father you need, with no penalty as liberty bells increase even when no founding father has been selected. There is still some luck involved in getting the right founding father but you can have some control over it.
Pro-tip #2 - Money raises so much faster when your in-land colonies no longer need to carry goods to your coastal towns, then your ships and then Europe or natives villages. Custom houses FTW.
All the money went to recruiting colonists, to create more settlements and make more money, to recruit more colonists... Being as close as possible to the unit limit is a must when you aim for high scores (but try not going over as it causes bugs like making your units disappear). Colonists that are inside a colony rather than the town gates are not counted when the game calculates the unit limit, so you want as many settlements as possible so you can house as many colonists as you can.
Pro-tip #3 - The more colonists you recruit, the more expensive it becomes to recruit colonists. The cost to train an expert miner however is always six hundred gold, so when the price to recruit free colonists is higher than that, it's cheaper to train expert miners until the recruiting cost for colonists drops back below six hundred, and if experts are offered in the Recruit window, always check the Train window and your colonies' needs to see if you're having a bargain.
Being the first independent nation multiply your final score by two (1.5 for the second nation and 1.25 for the third nation.) Halfway during my game, the English and Spanish attempted to declare independence before I did, I had to send armies and galleons in their most populous settlements in order to capture their colonists and bring them back in my colonies so they would not have enough people to declare independence. I let them reconquer their towns afterward, as defending these settlements would have been difficult during the independence war.
You'll want to kill some natives, and you should (Holy crap! Politically incorrectness!), their villages tend to occupy squares next to first quality resources, they'll harass and raid your stockpiles all the time, even when content, and the loot from Aztecs and Incas cities is a good way to hire colonists and kick start your money making industry but don't overdo it on higher difficulty levels because the penalty for burnt villages is multiplied by your difficulty level (one on pioneer difficulty, five on viceroy). Annihilating these two might be a good strategy on the easier difficulties but on the harder difficulties the penalty will negate any kind of monetary or scoring advantage you would achieve by doing that. Burn some to make room to expend your empire and kick start your industry, but don't overdo it.
So, let's recap:
You want a lot of colonists, cram them in settlements and get as close to the unit limit as you can without breaking it.
When you can't have any more colonists, train them, experts and skilled colonists are worth four points, free colonists are worth two points, servants and criminals are worth one point.
When you can't train any more colonists, you want more gold. You get one point for every thousand of gold in your coffers. A good money making industry, with lot of colonies, lot of industries and lot of custom houses should generate you more than ten thousand gold per turn.
You want to be the first nation to achieve independence to double your score.
The sooner you achieve independence, the better. That concept sounds good on paper, but if you can generate crazy tons of money or find a way to overcome the unit limit and hire more colonists, it's better to wait since the bonus for these two will be higher than the bonus for early independence. I recall seeing scores from pro players which gathered a little bit under one million gold to get that nine hundred points bonus.
Each founding fathers in your congress are worth five points, get them all for 125 points.
If the rebel sentiment in all your colonies is at one hundred percent, that's another one hundred points, plus it will prevents Tories uprisings.
Liberty bells generated during the independence war are used to summon the foreign intervention. When the foreign intervention has been summoned, every one hundred liberty bells generated is worth one point. You can get a maximum of one hundred bonus points this way by generating ten thousand liberty bells. Don't generate 32768 bells this way, not only it is useless to go over ten thousand bells, but when you reach 32768, the next bell will revert the counter to -32768 and you will lose your bonus. I found that the hard way.
Don't burn too many native villages on higher difficulty levels.
And last but not least, if you're trying to see what your citizens will name in your honor, you must play on higher difficulty levels. I don't remember if your difficulty level affects your score, but I know it affects the reward, for the same score, governor and viceroy difficulties have bigger rewards than pioneer or explorer.
Oh yeah, my soldiers have no guns nor horses in that screenshot because as my victory over the Royal Expeditionary Force was assured, I slowly disarmed my soldiers to sell the horses and guns for extra gold.