Advice to men trying to stretch out their groins and hips: “Don’t go into the pain cave. Your animal totem won’t be there to help you.” OK then.

Actually, that's good advice. Feel the stretch but do not go to the point of pain.

I like the Grok Squat.

The Grok Squat is very similar to a catcher’s stance in baseball. Simply squat down until your butt touches your ankles. Keep your heels firmly on the ground and your back straight. Hold that position for 30-60 seconds. You should feel your hamstrings, quads, Achilles tendons, lower back, and groin gently stretching. If you’re super stiff, it may take a few days of practice to sink into a full squat. Keep at it. Your back and hips will thank you.

Intersperse a few short squatting sessions into your daily routine.

Table pigeon pose and couch stretch also seem useful. 

See article for full description of these stretches.