First of all, why do I suspect APT is the fault rather than tight hamstrings? Given the attachment point of your hamstrings at the rear of your pelvis, if you are in APT then your hamstrings are in extension in your resting position. If you consider a pike with APT vs with posterior pelvic tilt (PPT) then you will clearly note that in PPT your pike will be more closed without any change in hamstring length. The following article describes this well:
There is another reason to correct APT, and that is that excessive APT causes thoracic kyphosis to counterbalance the arch in your lower back. Essentially, the S curve of your spine becomes exaggerated. An S is important, especially in acrobatic arts, but as with all things, excess is bad. A kyphotic thoracic spine causes your shoulders to be closed which makes hand-balancing all but impossible without arching your back. So correct your APT and you’ll improve two circus skills for the price of 1!
So why do you have APT in the first place? Weakness. Don’t feel bad, most of us in the modern sitting centric world have weak posterior chains. Your hamstrings, glutes and piriformis are weak, so when you excessively stretch, they get scared that they won’t have the strength to recover you from such extension, and so spasm up to protect you. As you can see from the following link, If Piriformis is spasming, then it is no wonder your sciatic nerve is firing:
So what to do about it?
Remedial massage: you can do this yourself with a tennis ball:https://www.youtube.com/watch?v=pxeHanoRW5s
This Piriformis stretch:https://www.youtube.com/watch?v=wT4948tW2hw
Another one I like to do I can’t find a video for, but start in the position of a kneeling hamstring stretch. So kneeling up with one leg straight out in front of you foot on the floor. Now staying tall, pull back the straight leg, keeping it straight and in front but rotating your pelvis back as far as it will go without twisting. Now rotate the straight leg out from the hip (keep the leg in front of you, you are externally rotating so that the outside of your leg is facing down.) now bend over forwards as for the hamstring stretch. You should feel a stretch in your glute and ITB.
Follow up with hip flexor stretch: https://www.youtube.com/watch?v=qHwyBHS6MQs
And this hamstring stretch: https://www.youtube.com/watch?v=CrF2iMnn09w
This should provide some relief, but to really excel, you’re going to need to strengthen your posterior chain to have better pelvic control. I recommend the following:
Pilates pelvic curls: https://www.youtube.com/watch?v=-fDXOEAqyts
Kneeling hamstring curls: https://www.youtube.com/watch?v=d4rXm7D2_SM
Glute Bridges: http://redefiningstrength.com/best-glute-exercise-glute-bridge/
Good luck and I hope this helps. If any stretching you are doing is causing you excessive pain or nerve discomfort, stop and try something different.