Does anybody know what I'm talking about? I'm intrigued by the idea of ancient cultures overlapping but I can't seem to find any information on it. I'm really only asking out of personal interest, I have no background in history.
I'm no art historian, but I know the style you're talking about. There's this statue of the falcon-headed god Horus in Roman military gear (with his scale shirt [lorica squamata] resembling feathers), it's not that really recognisable realistic style, but it's still pretty recognisably Roman. The god Serapis (a combination of Apis and Osiris with elements of some Greek deities) is generally depicted in Hellenistic style, but without any particularly Egyptian qualities. Isis was also adopted by the Romans, and had statues where she was only really recogisable by what she carries. Here's Anubis in Greek style too (I think this is the closest to the kind of thing you were looking for).
The Greek kings of Egypt also had statues in various styles. Unfortunately I can only seem to find clearly Egyptian (though this one seems to have a little Greek influence to me) or Greek-style depictions, though I'm sure I've seen more mixed depictions somewhere. I found one ring with a Hellenistic style depiction of the king wearing the traditional Egyptian double crown.
Another pretty cool example of synthesis between the different cultures are the Fayyum mummy portraits, which are portraits placed on the faces of mummies (which is a pretty Egyptian tradition) but done in a very naturalistic Greco-Roman style.
Like I said, I'm no art historian, but hopefully I found enough images in various styles for you (and didn't misinterpret them too badly).
EDIT: One more Roman Horus, a Romanised tomb painting, and I managed to find a very Greco-Roman statue with Egyptian clothes. The statue represents Antinous, the Roman emperor Hadrian's lover, as Osiris. His pose, head-covering and kilt are Egyptian, and the kilt looks quite stylised compared to the rest of the statue.