Keep in mind that Colt, GM and H&R did not fabricate furniture, they all had contract companies make grips, stocks and guards, among many other small parts. The three companies were only tooled up to actually fabricate 12 major components of the rifles. They did fit/finish work, assembly and testing in house, but really the majority of parts were subbed out.
Back to the grips, the thing that stands out is that, in general, Colt had skinny grips with a myriad of different markings.
GM and H&R had fat grips. GM with the cross symbol, H&R with the large single number.
I have never seen a factory Colt rifle with a fat grip, nor have I seen a factory GM or H&R rifle with a skinny grip. I'm sure, as with many areas of retro history, there may be exceptions, but these are my observations, and seem to follow the general consensus here.
Unfortunately there isn't a guide for this stuff yet, but I think we, as a community, are getting close.