Pain in back pocket
No, it doesn't change anything. I ignored what you said about the gap between RH inner thigh and seat post sitting further away from the seat post because based on what you had already told me, I assumed you were mistaken.
Another thing; when you say that it has twice been confirmed that there is no leg length difference; how was this determined. If it was by measuring from bony landmarks, then understand that the even if the person knows what they are doing, there is a potential measurement error of plus / minus 5mm. What I'm saying is that external measurements are not definitive and are more of an educated guess. So have that X ray. You will need a front on shot (make sure knees are locked) of the pelvis with the relative height of the femoral heads noted (not really concerned about what happens below that and will explain if necessary) as well as a side on shot so that it can be determined whether both iliums are in the same plane.
To clarify, I don't know whether you have a short leg but it is worth finding out. Even if you don't, try the shim. If you are dropping the right hip because you are significantly tighter on that side, a shim can work a treat to give you relief while you work to redress the difference in range of movement between sides.
On that subject, do you stretch much?
If not, start. Two really good self help books for people with problems are " Stretching and Flexibility" by Kit Laughlin and "Stability, Sport and Performance Movement" by Joanne Elphinston. Lastly, most people who do stretch have poor technique and a distorted view of what they are trying to achieve and how best to go about it. Read this link, particularly the contribution by Dave Fleckenstein, for more info on the most effective way to stretch -http://www.cyclingnews.com/fitness/?id=2008/letters04-30#8
Have fun!