Yes, that was the top of my list of suspicions.
Kurz comes well recommended for stretching information, so I think you do well to reference him. Anterior pelvic tilt sounds correct. Just so we are on the same page, we are talking about tilting the pelvis and increasing the extension/arch of the lumbar spine/low back. Effectively this points the zipper (or where the fly/zipper/front seam of your pants) more towards the ground than forward when you are in the full side split position. This alone may be enough to open your hips.
The cues I have found to work are the pelvic tilt, stretching other muscles first, and pushing the legs/feet out.
I wrote earlier about stretching the hip flexors first. I just do a kneeling hip flexor stretch and then pull my ankle up behind me to hit the quadriceps. Then I perform a hamstring/stretch the hip extensors. Finally I stretch the adductors. At some point I also like to hit internal rotation of the hip. I would certainly want to stretch all of those before working a side split, though I understand if you are doing this as part of a class you may not get to pick the order.
The single best cue I use is to visualize/try spreading the walls or floor apart with my feet when in the stretch. I write cue because obviously I can't do this, but by focusing on spreading the floor rather than dropping down or abducting my legs my body seems to take care of the pelvic tilt by itself.
If you have material by Kurz you can just follow his instructions. Just this caution: In general try to position your body so you feel the tension in the muscle bellies, not across or around joints. Femoral acetabular impingement can lead to damage of the joint and has been linked to early onset arthritis. Avoid causing pain in the joints. Also, you never wrote why you are pursuing the full split. If it is for martial arts or gymnastics be aware that other movements can also lead to impingement and make sure your mechanics are correct in those at well.
I hope this was helpful.