Health- Bishul akum is when a goy cooks all of the food without any input from a jew. According to ashkenazim even lighting the fire is enough. For sephardim, the jew has to actually take part in the actual cooking, but not the whole thing. So if the crockpot was on and then got turned off, it for sure cooked something under a jew’s hands. That’s why he doesn’t think that it’s likely to be a problem of bishul akum. Only if it was completely raw it would be a problem, if it was in a crockpot. On the fire, an ashkenazi can be meikel from that point.
However, if the cholent is cooked partially-but not ma’achal ben drosai- before shabbos, you would have a problem of shehiya even before shabbos started.
The problem of amira leakum is simpler. You cannot tell a goy to do a melacha for you on shabbos.
So as long as it’s not fully cooked, or it’s cold, it would be a definite Issur.
I’m assuming that you can get around the amira leakum problem, though. If the chulent is fully cooked and gets turned off in middle of shabbos, if it’s still piping hot, or according to ashkenazim, not cold yet, a goy would probably be able to put turn it back on (trei derabanan letzorach mitzva). For sephardim, I understand that you can simply move it yourself into a different pot as long as it’s still hot and put it on the fire.