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I get a very different result for a specific example of the case above.
For a frictionless quarter circle of radius h = 100 feet, I find the travel
time to be 3.27757 seconds (I needed to solve an integral numerically in
Mathematica - if someone can direct me to a closed form solution that
doesn't have elliptic integrals in it, I'd be most appreciative). I assume
the quarter circle is oriented so that the initial part of the arc is
vertical (aligned with the uniform gravitational field) and that the end of
the arc is horizontal.
For an inclined plane of slope 1 with a vertical drop and horizontal
traverse each of 100 feet (ie an inclined plane between the initial point
and the final point of the quarter circle arc above), I find the travel time
to be 5/Sqrt(2) = 5.5355 seconds.