This allows to use fewer evaluations (30 msec down to 23 for me) while giving more accurate results (3x-10x less relative absolute error) compared to classic ray marching.

Not a massive difference, but meh, it's better. For Cycles the speedup doesn't really matter much, but I also have a patch for Eevee support.

I've also tried Gauss-Legendre and Gauss-Lobatto - the latter was always worse, while the former was slightly better at 2deg elevation but notably worse on 15deg.

Unfortunately the same approach can't be used for the integration along the primary ray, since there we also need the accumulated transmission so far at every integration point, not just the total result.