This page has a list of low to medium carb American beers
Unfortunately Carbs equal taste in beer, so most of these beers are pretty light in taste.
My best bets for flavor are the one that is not really a U.S. beer, Amstel Light, and the one referred to as "amber" which is Michelob Ultra Amber...usually Amber=more flavor when dealing with non-IPA type brews.
Honorable mentions would be Coors Light, regular Michelob Ultra, then MGD64 in order from most flavor to least. I haven't had MGD64, but MGD does have more flavor than regular Miller beer. The rest are not very flavorful, but are still beers and will provide some "beery" flavor to a dish. A lot of people drink those beers not because they are on a diet, they actually just dont like what real beer tastes like so they drink the girly versions! I could catch some flack from some guys on that comment...there are a lot of guys that consider themselves pretty macho that drink these light beers. I'm a craft beer snob...so take my opinion at that, my bar is really high. The best beer is Belgian, but our craft breweries in America are making some outstanding drafts as well.
1 cup is 8 oz liquid, those beers are listed at 12oz. Amstel light at 5g carbs for 12oz is 3.33 grams carbs for 8oz, divided by 8 servings in the original recipe is less than a half gram carbs per serving from the beer. Same would be true if you halved the recipe, and of course halve the beer along with it.
So, you CAN cook with beer and be low carb, just not really good beer!
I just bought some xanthan gum for thickening, but I haven't used it yet so I cant tell you the best way on that yet.