I have added some interpolation methods to help avoid some of the weird stretching you get with reprojection, but they're only available in the python version because they rely on some large scipy packages that would be tricky to fold into the .exe version, and they also work a lot better with original heightmaps rather than full color images. With the upscaling-downscaling approach, the results may depend a lot on the interpolation your image program uses--a lot default to bicubic, but that can sometimes create issues on sharp boundaries.

Overall, I'd say in any scenario where gprojector meets your needs, you should stick with it (also check out some of kunimune's tools https://github.com/jkunimune/Map-Projections), I built projectionpasta to cover various edge cases: very high resolution, 16-bit heightmaps, and direct projection between 2 oblique aspects or from unusual input projections