I tried Loose Files and American Scramble, and I thought it was like most Andy Callan efforts: a lot of great ideas that needed work.
To expand a bit on Timmo uk's oblique reference, British Grenadier is a more mature game system combining concepts from LFAS and General de Brigade. It's expensive now (only available in the Deluxe version) but if you live around GdB or GaG players, it might be an easy sell.
I also recommend trying Guns of Liberty, a great little game focused on the AWI period. It's fairly simple and straightforward, essentially a mashup of classic horse & musket gaming mechanisms, pretty easy to learn and teach. Currently you can only buy it directly from Eric Burgess, though he's recently said he'll release the 3rd version as a print-on-demand or PDF or something. Since version 3 has been about to be published any year now since at least 2012, I wouldn't wait. :-)
Winston Smith/John the OFM is a strong advocate of using TSATF for the AWI. If you like TSATF, that should work just fine, and if you have a lot of TSATF fans to play with, it's an excellent choice.
I settled on Regimental Fire & Fury, and I have a web page dedicated to my house rules for it. RF&F is no more "perfect" than anything else listed so far, but I like it about equally to GoL, and I have a larger pool of experienced RF&F players to recruit from, so RF&F is what I play.
All that said… I don't know that any of the above will do a battle as big as Monmouth in an evening. Of all the suggestions in this thread so far, I think only Volley & Bayonet and Black Powder may match that requirement. You might also take a look at Koenig Krieg and Warfare in the Age of Reason, both of which were designed with large 18th C. battles in mind.
Another idea I've toyed with but have yet to try: adapt Fields of Blue & Grey to the AWI. These rules are morale/disorder-driven rather than casualty-driven, and represent each battalion/regiment on the table while using the brigade as the unit of maneuver and morale. Those concepts are the right approach to get a battle like Monmouth done in an evening, but whether FBG works well enough, I can't say yet. FBG is free, so you can't beat the price. ;-)
Edit – Do the Black Powder rules give a good feel for the AWI?
Of course they do, but absolutely not. Do you really expect to get get a useful answer to that question on TMP…?
To really answer your question, you'll first have to define what the "feel" of AWI comabt was, and I think a lot of us playing the period are still working on that. Try reading With Zeal and With Bayonets Only and figure out how to translate that to a miniatures game, and best of luck to you, sir. Meanwhile, if you like the BP mechanisms and accept the abstractions, you'll probably like AWI BP just fine.
- Ix