Here’s a set of free wargames rules for the American War of Independence.
DBA For AWI is a set of DBA modifications for the American War of Independence.
Standard Wargame Rules For Ancient and Medieval Warfare is an alternative to DBM with the same basing. The authors write:
The designer team includes both extremes of wargamers: dedicated tournament players as well as those who prefer historical re-fights. These rules aim to satisfy these both sides of the wargaming hobby. We wanted to write a set of rules that allows playing realistic and interesting re-fights of historical battles. Furthermore, we have spent much time to make the rules as exact as possible, so that they are also suitable for tournament play. Once both players know the rules, there should be no need for an umpire or for long rules discussions during the game.
One aim was also to design a rule set that is “easy to learn but difficult to master”. This means that you can learn the rules relatively quickly, but will probably need several games, before finding the optimal tactic for your army. Also, there are no “super troops”. Each troop type has certain strengths and weaknesses that you will need to learn.
Wargames Rules 1685-1845 is a set of classic WRG rules from 1977. I own a copy, but you can get your own in pdf form at the link.
City Grounds is a fantasy skirmish game in the vein of Mordheim, but with different mechanics.