So I have a question. If Isshin is from SS then how did a dead man produce children? Do we believe the gigai have the ability to produce offspring when inhabited by a soul?? I don't believe that.
So I now propose that Isshin is human and one of the humans which Ukitake referred to when he gave Ichigo the Combat Badge.
So what about the shihatso? We don't know how he got that. He could have gotten shimigami powers from a captain back in the day, similar to how Ichigo got power from Rukia. If he got powers from a captain maybe a form of captains robes appeared on him when he transformed to soul form.
Also I think Kurosaki is actually his wife's last name