High-frequency propagation along and near a concave boundary excited by a source close to the boundary exhibits anomalous effects attributable to the failure of ray theory for the high-order multiply reflected fields. For moderate values of the universal parameter γ = (ka/2)1/3s/a, where k is the wave number, a is the boundary radius and s is the propagation distance measured along the boundary, suitable alternative field representations can be established by hybrid forms that combine legitimate ray fields self-consistently with whispering gallery (WG) mode fields and/or integral remainders. These previously established formulations become problematic where γ gets to be large, as happens for long propagation distances or very weak surface curvature. Modified hybrid options are developed, which can cover all phenomena near and far from the boundary, for small through large γ. Of special interest is a new ray-parabolic equation (PE) scheme wherein the WG modes in the boundary layer near the surface are replaced by a beam-type propagator. PE can be implemented numerically by a forward marching algorithm and can be adapted to variable curvature boundaries, including concave-convex shapes for which the other options fall. Extensive numerical comparisons reveal the validity, utility and limitations of the various alternative field representations.