I doubt the water scenario would be the case- flight path, speeds and altitudes in the plot don't seem to indicate that (to me anyway). One would expect a steeper climb, more rapid speed loss, then stall. Divergence like what is plotted from centreline as soon as it lifts off is not very likely to indicate a CofG issue, in my opinion.
It's been a while since I've had the guts out of a B200 but from memory water wouldn't exactly flow to the back so rapidly. If I moved a large passenger from the front to the baggage compartment during rotation it wouldn't result in this.
Horatio, maximum fuel imbalance in a B200 is 1000lbs. If it is fitted with wing lockers the imbalance is reduced, if memory serves me well it's by the capacity of the lockers which I think is about 300lbs- don't quote me though it's been a while.
Have flown them with 500lbs imbalance. Not a big deal.
Sideways during the takeoff roll DF? Interesting. Any idea as to how accurate that is by way of was it all three wheels on the ground or it was already rotating and its then started to go off the side whilst getting airborne?