"By my books" referred to a search on the nihonto signature repository.
50 years and three generations and not sure how much online archives cover the signatures. But the main problem is that you came to a conclusion from whatever you were looking at of Sho-shin.
But Fujishiro doesn't document him having SAKU in the mei. Nor does any papered example that is Juyo, Tokuju, Jubi, or Juyo Bunkazai.
This isn't meant as criticism, this is meant as something that will save you tens of thousands of dollars if you remember and learn from it. We need enthusiastic guys to not blow themselves up on fake stuff early then depart. Usually people who blow themselves up on bad stuff depart because it's hard to face the reality of their decision making and it's easier to blame the entire hobby as being corrupt. The reality of it is that all art, antique and collectible fields have predators and also they are prone to differing expert opinions.
Predators will take advantage of you on known bad stuff. Other experts can respectfully disagree, one saying this is no good, another saying it is good and you end up trapped in the middle. If you want to emotionally take the case of one expert always trumps the other then it's a fight to the death. Whereas you should probably listen to individual arguments and side with the guy who has the best argument on a case by case basis (i.e. if you see a parallel to politics here, yes there is one).
Anyway back to the Motoshige, what you need to do on a signature is first at least read it. In this case it reads out with the SAKU on the end and then you check Fujishiro and see if Motoshige signed with SAKU according to him (answer: no).
Next search Nihontoclub and see if you can match the signature:
Before we've even gotten to checking the mei, it's ruled out because we're being forced to choose between zero examples ever being seen in the history of Japanese books (which these other sources have accumulated) vs. this example being a super rare real thing. Occam's razor applies.
If you want to then be extra careful you check all modern examples to see just in case if something popped up that wasn't historically known and the answer again is no (i.e. what I did, looked at all the books, for which you need the books).
From there you now basically have zero reason to believe this thing. That you didn't end up here means that you need to look at and modify your methodology.
Now we can look at the strokes of the mei.
Without even going to the books I can tell you that Ko-Motoshige signed in two characters and is an Aoe smith, and this isn't him because it's not two characters. Also his mei is kind of funky looking.
And then I can tell you Nidai Motoshige he signed in small characters so this is no good again on those grounds.
Nidai Motoshige also has a clear preference for signing in the shinogi-ji and if a nakago has a shinogi and the mei is not in it, then it's questionable. Because this is orikaeshi it is hard to know where the mei was, as you'd need to unwrap it. It looks to me like it is too big to fit in the shinogi-ji though.
So it leaves it possibly as a Kamakura period Shodai Motoshige work.
the intuition that inlaid signatures are less likely to be fake
As soon as one single person has that intuition, a faker will make a fake mei on a sword just before shortening it and then will make orikaeshimei from his fakery.
Your assumptions and your greed are weaponized by fakers. You need to as a result get rid of assumptions that are not based on reasonable arguments. It will be less likely that a maker will go to the work of making an orikaeshimei fake because he could fake another mei or pull this off with less work.
However, if the work was just faked a long time ago and then someone later on honestly preserved it, this is what you get from that.
So there is no reasonable/rational argument that says orikaeshi means it's less likely to be fake. All it means is that it happened earlier in time to the shortening. 10 minutes, 10 years or 100 years, you be the judge. Anyway as such you need to ditch that assumption and just go on the basics.
Note again that in the modern period with power tools the work needed to do an orikaeshi is a lot less than it is in the Edo period. So if you wanted to take advantage of someone and shift the mei back in time, you would do this in the 1900s some time with a few hours of effort on an obviously gimei Motoshige that you found.
Now you have done two things:
1. they made the gimei look a lot older by implying that the orikaeshi is old, and so the viewer shifts the time period of the signature back enough that it seems legitimate
2. they give the impression that someone cared about this signature so much in the Edo period that they preserved it. As the phantom menace reviews say, "You may not have noticed it, but your brain did." This causes you to abandon some of your own rational processing by embracing the perception of someone else's opinion in its place. i.e. you punt.
While he is waving some scarf around in your face, the street magician is undoing your watch with the off hand. This is why you don't let yourself get too distracted by some of these other things, if the primary stuff is not adding up.
Now we can look at the characters and compare to a known good example of 1st generation Osafune Motoshige.
Bear in mind, this thing has to do a LOT of convincing because it's not even a documented signature style. Nidai is absolutely ruled out as it doesn't match the size, style or placement of the characters, Ko-Motoshige is ruled out on the same grounds. We just need to see if this is Shodai Motoshige.
Now look first at the Shige 重 character in the two good mei.
The two good examples, this feels wide and fat. Chogi's mei is like this too, the same impression. The candidate feels square and normal.
Look at the Moto 元 character. The left bottom leg terminates halfway down in the candidate. That looks more like Kanemoto's signature. Also note that the right leg, the L bend in it is angular in the two good examples. In the candidate it is rounded.
There are no grounds for accepting this signature at all, unless you want to accept:
1. using an undocumented mei by characters
2. doing the characters differently
And if you want to accept both of those then basically I could sign this with my own name and we can say it's Motoshige as well by those rules.
Since we can't see the other half of the signature, we should assume the worst on it.
The flip side of this is that as long as the blade is a koto blade you can wipe the signature and maybe it papers to someone good (maybe even Motoshige!)
So that's the analysis route that you'd need to go if you want to believe in one of these. That's why I drew attention to "your books" as I didn't see where any references could end up with the assumption that this signature was ok.
Start by assuming it's fake and force it to convince you.
If you bid on it, as long as you do so with the assumption that the mei is fake, it's ok. If you think the rest of the work is good and you don't spend more than on a mumei speculative piece.
I did this on a daisho and the tanto ended up being a lot better than the mei and the katana ended up being a lot worse, and it kind of washed out for me. If I did more research beforehand maybe I wouldn't have bid on it.