I enjoy primarily prototypical models, but there certainly is nothing wrong with some "what if's" now and then. Mehano/IHC made an HO GG1 in a modified Milwaukee Road paint scheme, which is conceivable if a GG1 could have been made to run on the MR electrified lines. The IHC box label generally calls it a GG1; but one variant label actually calls it a Little Joe!
Apparently, the New Haven EP-3 was loaned to the Pennsylvania for study, and the GG1 has been described as largely an EP-3 clone with a streamlined, Loewy carbody. What with New Haven and the Pennsylvania teaming up to form the New York Connecting Railroad responsible for building ****'s Gate bridge, and also teaming up to run the through trains from Boston to points south of Manhattan such as Philly & Washington, DC, and as the New Haven had substantial catenary lines. MTH did an East Wind set, with a GG1 on point -- a joint project between the Pennsylvania, New Haven, and a few other cooperating railroads, with service from Washington to Portland, Maine. So it also seems entirely plausible that the New Haven might have acquired some GG1s at some point. (Okay, I know they did not really acquire any in fact -- just not as farfetched as, say, the New York Central acquiring a huge engine from another railroad that was not only a bitter competitor, but would not have fit through their older, lower-clearance tunnels.)
There have also been GG1s made by a few different HO manufacturers in the McGinness scheme.
In a future O gauge catalog, it would be fun to see a GG1 in the Cranberry paint scheme, or the green top/orange bottom with pinstripes, for example.
So, to each his own -- whatever makes you happy!
David