Bike fit / correct riding position

When it happens, it feels like the muscles surrounding the point at which the spine connects to the bottom of the V formed by the hips become tonic/do not release/do not get enough bloodflow/have significant lactate build-up or something along those lines.

This sounds like exactly what I have, albeit maybe slightly higher up the same group of muscles. They start feeling stiff, contracted and painful over longer distances.

My bike fitter pointed out excessive movement in my lower back during the pedal stroke as the key and suggested that the glutes were not doing their job of stabilising my back. This caused the back muscles themselves to try and take up the slack, hence the pain, stiffness etc.

The solution was stretching and glute exercises (single leg glute bridge, clamshell etc) more than bike adjustment. There does seem to be some improvement if I do these both before and after time on the bike