I stretch my quad in a lunge position on the ground. I'll put my left knee on the ground and my right foot on the ground out in front. I'll gently pull towards my right foot stretching the left quad. I try to make sure to have my hips forward as this helps to keep the quad stretched. I imagine pushing my left hip forward and pulling my pelvis under me (like... not sticking my butt out.) I'll hold it for about 30 seconds. I'll repeat on the right quad.
does that make sense?
I don't know if it stretches the quad to the same extent but i find it to be sufficient.
Sometimes i lie down while stretching my quad the way you describe as i can focus more on stretching the quad without pulling the knee too much.