Emily's experiene is similar to mine. This was a particular aggravation when I combined heavy cleans or DLs with long hours sitting, especially in the car, where mobility is particularly constrained. The stretch that does the best for me is a psoas stretch
(think sampson stretch with a 45-degree turn and gentle bend away from the rear leg). (It's suprisingly hard to find a decent image of this particular stretch, given how easy it is to find stretches for the so-called iliopsoas that don't do as much for the psoas, because the iliacus takes the brunt of the stretch.
Glute stretches that are a variant
of pigeon pose
seem to help as well. There's little doubt that having more flexible hamstrings couldn't hurt me either.