I think that you can look at the market to see where the crossover
occurs.
THere are currently no production piston aircraft engines over 450hp
and
there are no aircraft turbines under 400hp.

There's lots of ground turbines under 400hp so we know there's a market
there; [...]

A ground turbine runs at almost constant speed, near its design point,
so even at small dimension can still be fuel efficient. Part load fuel
consumption of a gas turbine is a bit too high, particularly for GA
aircraft (considering their flight pprofile).

--
Fritz