[leguminous]

I have done something like this with a Lanczos kernel (a=1) downsizing repeatedly by 2x, a small Gaussian kernel, and then repeatedly upsizing by 2x with simple hardware bilinear sampling.

The (2D) Lanczos downsizing can be done with only four samples using the bilinear sampling tricks that you mention, and I avoided expensive trigonometric functions, divisions, and the singularity at 0 by using an even 8th order polynomial approximation. I would be curious to see the results using this kernel, but the Lanczos is so far the best that I've tried.