Those "inconsistencies" were taken from the affidavit, we don't know what any of those people really said. The affidavit is what the affiant has paraphrased as best they can recall, essentially it is hearsay. It is not first hand and may not be correct. The only correct statement/version are those made directly by the people involved, and as far as SA is concerned that has not changed.
There are significant reasons to believe that the affidavits may not be accurate, since they do not provide any specifics about what SA said, only what they understood him to have said. For example, when they talk about SA's trip from work to his mother's house, they provide no details except that that was where he went eventually. It implies that they didn't ask specific details about the trip, such as which route and how long it took, stuff like that. You would have expected a diligent investigator to ask questions like that, but they apparently did not, at least they have given no indication that they have. If they did, they would have included that as direct solid evidence that he was being untruthful in the affidavit if he said he took route X, but phone records put him on route Y. But there is nothing like that, and all through the affidavit, the supposed lies are in a similar vein: no detail about what SA claimed. Instead it was inference by LE compared against evidence from other sources, and from that basis LE concluded that he was lieing.
As an exercise in logical argument, this is very troubling.
I have been pointing this out from when the affidavits were first released. Much later SA has been interviewed, and his version is they didn't ask these specifics. His timeline is reasonable and is in agreement with what we know from phone call routing records pinging back to various towers. So, I'm inclined to give him the benefit of the doubt about that.
Now, what did he say in the actual interviews? Hopefully LE recorded those, and if so, it will be very clear if SA changed his story or not. But for now, in the absence of those recordings, and the clear lapses in the affidavit, there is no way anyone can say the story has changed, because we only have one version.