Kajihei is a special case, but it's worth noting that while gimei have always been made, many of those found today were made recently, and are called gendai gimei.
A well-engraved signature is by no means a sign of legitimacy. There are a few (papered) examples available on the net. Personally, I think the mei is a little too far to the right, but that's just an impression.
Yasurime are yasurime. I do own a sword with gyaku takanoha which is pretty rare but it leaves me cold; having said that, as it's a suriage and mumei blade, it helped me find the blacksmith.