There are already implementations of sample sorting that are much faster than c++ sort (but I don't recall how much faster). I'd be very interested in a comparison to some of those...
Also, since we are sorting integers, I'd also be interested to know how well a modern implementation of radix sort can be made.
We integrate vqsort into ips4o, calling it once subarrays fit in L2. That speeds up ips4o by 2.9x (single thread) and 1.6 (parallel - bandwidth limited). More details in the paper.
I previously also worked on radix sort: https://arxiv.org/abs/1008.2849 Interestingly, that 12 year old result on dual-socket/8 cores is only about twice as fast as a single AVX-512 core today.