Hi, Just thought I would throw in my thought incase it may help you solve the issues and get back on your bike.
Whilst 'core stability' has been very fashionable for a number of years, I think what the previous post is getting at is that training your 'core' in its' most obvious sense (i.e. doing hundreds of crunches) is a bit of a misnomer. Of course we all have enough abdominal muscles to hold ourselves upright etc, but that is missing the point, and concentrating on the wrong muscles and systems.
Over here in the UK I run a bike fit and physiotherapy service specifically aimed at cyclists and the problems we are prone to. I started the business as many people can fit you to a bike but have little idea on how different peoples problems need to be taken into account when fitting a bike. There are also sports therapists and other physicians who are very good at treating the symptoms you may experience but post treatment if you simply get back on a bike which is poorly setup you will quickly be back at square one.
So, back to 'the core'. From the information you give and obviously it's difficult without actually seeing you, it sounds like you do have a problem controlling the forces that riding a bike places on your pelvis and lumbar spine. I agree that these forces are not as great as say, running, but can still cause major problems if not properly addressed.
I see many people who have either a lack of force closure of the Sacro Iliac Joint or poor muscle control meaning their spine rotates during every pedal revolution. Both different conditions with different fixes but with similar symptoms.
In an ideal world your spine and pelvis should be a really solid, locked down structure, this then allows your hips and legs to move independantly getting the most out of your pedalling. If you think of your SIJ as a key stone at the top of an arch between the bones of your pelvis, if the joining surfaces don't mate together well then your will have a loose platform, with your pelvis shearing on either side. Now imagine that happens every single pedal stroke over a 2 hour ride or longer. This is even more important given the amount of nerve roots you have in the area. The same can be said for a lack of control of the small muscles that hold the individual levels of your spine. If these are not switched on and your spine rotates just a tiny amount, when this happens over and over again, it's easy to see how nerves can be irritated and leave you in pain.
As a knock on effect of these things other muscles will tighten and even spasm as compensation, this may mean cramps in your hamstrings or painful aching in the larger muscles of the back.
I have had a lot of success by giving people a focused programme of exercises for their specific problems. Obviously it would be best to be able to see how your body works when on the bike, but let me know if you would like to try a more generalised programme of excercises.
As for only seeing someone with a particular piece of equipment, I would be careful. I honestly believe that even the "perfect" fit will not necessarily overcome your issues so don't pin your hopes on someone with some space age technology. I don't use the Retul system yet, although it does interest me as an additional resource. However, using slow motion cameras and my experience I can see a great deal of how tiny movements are effecting people when pedalling.
Sorry, I have waffled on far too long now, I hope some of this has helped. Let me know if you would like any more advice.
Good luck with it all.