Using the runway to get to V-mini and letting the autopilot do it's thing would have prevented this accident, IMO. Instead, whomever was flying got rushed, spatially disoriented, overrode the autopilot (not sure if they ever even reached V-mini, so it wouldn't have mattered) and did not reference the instruments.
The docket says the force trim release was engaged from TO to impact. The autopilot was probably never flying but it was set correctly set to indicated airspeed and heading.
The one pilot said he didn't want to use the hat for takeoff and also released the force trim. A terrible idea in those kind of WX conditions and the kind of takeoff it sounds like they used. They also probably felt rushed because of the situation with sick passengers needing medical attention. Everything lined up for a tragic outcome.
I don't understand why the pilot monitoring pretty much just watched the whole thing happen.