Given the big differential in troop class you describe I’m not surprised the Americans can’t win a game, all else being equal.  Rules use class to cover the differences in quality and performance between troops and so create sufficient variation between forces to make a wargame less chance based.  One way some rule sets try to even things up is with leadership classes that penalise poor commanders and give bonuses to good ones.  I don’t play British Grenadiers so don’t know if this is part of the system.

If your historical refights can’t return the correct result on the day because of this rules imposed restriction then it needs changing.  Not everyone is a fan of house rules but your situation seems ideal for it.  I’ve played scenarios with temporary penalties or bonuses to class that are scenario specific.  Milita units get +1 class and to reroll failed morale tests if they occupy their village, regulars get a morale penalty because they didn’t get paid or ran out of rations, local skirmishers get enhanced cover bonuses regardless of the terrain they occupy, etc.  One set of rules that has a good period feel (although on a smaller scale) is Muskets and Tomahawks.  I’ve not played AWI but plenty of FIW and the way they handle skirmishers and scenario based bonuses and penalties is excellent.  They give a very good ‘period feel’ as far as our group are concerned.  Regulr units are tough and if everything suits them (open terrain, clear lines of sight and room to manoeuvre) they are hard to beat but the game features boards that are busy with terrain and careful use of this and good coordination of your units can see them soundly beated by the locals.