[nice_byte]

Author here. Please let me know if the sample code doesn't work for you. It's all single threaded dumb JavaScript which makes it very easy to read, but definitely not performant. I decided to stick with it for didactic reasons, but still worried that it may hang someone's browser.

[geon]

Would it be practical to use high resolution spherical harmonics as a replacement for cube maps?

[nice_byte]

Not really. Besides the problems with ringing outlined in the post, the number of coefficients required to capture higher frequency detail grows quadratically, requiring not only more storage but also operations to evaluate. Which makes straightforward cubemap replacement impractical.