GItrouble,
This sounds identical to a problem I have been suffering from for years. I haven't let it get the best of me yet as I'm still running/improving each year, but just like you I have considered quitting running because it's so painful and can last for quite a while.
I would say this lower stomach issue is worst on either my long runs or fast workouts. It's frustrating because you feel like you can't complete more than half the workout before you are sprinting to a bathroom only to find that you can't go to the bathroom, so you continue to try running and the same terrible pain/need to go comes back.
I'm not a doctor but I've described the problem to numerous doctors and looked up a lot of information. Many doctors have explained to me that hard running does cause trauma to your intestines/stomach because you are constantely bouncing up and down; depending on the person I think it effects some worse than others. Also, if you suffer from IBS (irritable bowl syndrome) then I believe this probelm is going to be even more aggrivated by running, esp. the hard workouts/longer runs where your body is under a greater ammount of stress. There isn't really a cure for IBS or the stomach problems but there are things you can do to minimize the terrible pains/spasms/cramping that you are feeling afterwards.
1. What are you eating before you race/do a workout/long run? It's good to eat plenty of fruits and vegetables but I would try to eat something more gentle probably for the 2 meals prior to your run. Things like a bagel with jam/pbutter and a banana are great. Bananas tend to slow down your bowl movements. Don't eat high fiber foods like apples/oranges etc. This will cause that noisy "blub-blub" noise in your stomach which will probably be followed by the cramping pain after you finish the run.
2. Make sure to be eating enough protein but protein can take up to 5 hours to fully digest so try to eat it near the end of the day (dinner).
3. The other guy's post about avoiding dairy was good. Try to not eat too much of it just before a run. I drink soymilk at breakfast and maybe have some yogurt after my morning run but I try not to have ANY milk/dairy at lunch before I go on my afternoon run/workout. Try to drink only water until you are done running for the day. THe reason is because teas/coffe/juices are diarretics and will make you have to go pee. This can aggrivate your bladder while you are running. I dont think the pain is always in the intestines; a lot of the time, I'll have to go pee bad while I'm running and then about 10 minutes later after I stop I have this HORRIBLE HORRIBLE pain in my lower stomach (near my bladder) and I can't always go after I run even though I have to. The only way I can feel comfortable is in the same position you said, or just laying on my back in my bed until it calms down which can even take up to 2 hours. I hate it so much because you feel like you can't even get up to eat or drink anything because it's so painful.
4. I stop drinking fluids at least 1 hour before I run. I'd stop about 1.5 hours ebfore a hard workout. As long as you have been properly hydrating, this is the best thign to do if you have such stomach problems. I usually eat about 2.5 hours before each run because this seems to give me the best energy/least amount of stomach pain.
5. Visit your doctor and see if they can test you for IBS or try to find a medication that may help. Usually there isn't one, but I did find a doctor who gave me a bottle of pills for people who suffer from chronic bladder spasms. She said I only needed to take it before I raced or had a hard workout/run. I would take it 30 minutes before, and honestly, it really cut down my symptoms. Even if I had to go during the run, at the end the stomach cramping wasn't so severe. You don't need to take it daily, just before hard runs/races.
Hope this helps you out; I definitely know what you are going through and I wouldn't wish it upon my worst enemies...well maybe some haha.
Let me know if I helped you out any!