At 350hp, I'm assuming a turbocharger, but I suppose even that might be
missing? In reality, it sounds a lot more like an SR22 or Columbia 400
to me. The
high wing might invite comparisons to the Extra 400, but it's pretty
obvious
the similarity is strictly aesthetic.

My guess is the Lyc TIO-540 from the Chieftain. I can't think of a
normally aspirated engine with that kind of power (a detuned IO-720?)
As far as the comparisons to the SR22 or Columbia, I think that was
pretty much their target, seeing as Cessna & Cirrus are essentially
tied for piston single production.