This is a nice result for the single-scalar case, but it is not immediately obvious to me how it would scale to support SIMD, given its use of per-element index

This is a nice result for the single-scalar case, but it is not immediately obvious to me how it would scale to support SIMD, given its use of per-element indexing and a periodic conditional fallback to a slowpath which does not trigger at the same time for all lanes. Extending Kahan summation (or similar techniques) to take advantage of SIMD, however, is completely straightforward. In the age of AVX-512, the speedups from SIMD are hard to ignore even for 64-bit precision arithmetic.