Yep, to fully correct fisheye lens distortion you'll need 4th degree correction, as that Stack Overflow comment thread suggests. But getting the K1, K2, K3, K4 values exactly right for the lens will be a challenge.
I've used programs called AutoPano Video Pro and AutoPano Giga that can take a series of photos taken with a fisheye lens camera, find tracking points, and derive lens correction values from those. The program can then be used to create equirectangular 360 or VR180 videos from action camera footage.
A 3rd or 4th degree lens correction video processor preset for Reaper would be rather quite nice! But the calibration will remain a challenge.
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