Not really a dynamic campaign type game, but it can sort of be played as such (especially if you're going the historical route of the standard American map) is Colonization. There's a good, free version of it called FreeCol that can be found here:
http://www.freecol.org/download.htmlWhile a Civ-like game, it's able to be played with a couple of different win conditions and isn't nearly as "war'y" as your average 4X game. Dynamic in the sense that everyone is your friend or your enemy depending on a massive range of factors and strategies, with these allegiances changing as the game progresses. FreeCol has a slightly different rule-set and some extra starting bonuses/nations (with Fur Trapping being a bit OP'd), but it does make for some fairly varied routes to winning.
Things to try: Arm the natives on purpose so they'll be a nuisance to your competitors.
Never sell a thing to your home-country.
Immediately take an opposing capital as your only or main city, letting England win with Ville de Quebec as their capital.
Convert every native village. Work out what the hell to do with the massive native population now under your command.
The game does have some rather worrying overtones, but the colonisation of the Americas did historically anyway. You can win quite easily without a single indentured servant or native convert if you want (and punish other civs that use them if you please), with options for full citizenship through founding fathers eventually possible.