YES.
It sounds like your psoas major is chronically tight (like you mentioned) and it is pulling your Ilium out of the ideal alignment. This will cause the following symptoms:
1. your ASIS may feel lower on that hip
2. your adductors will be shortened and chronically under tension and most likely not respond to normal stretching like your unaffected leg does
3. tight inguinal ligament
4. Toeing out during gate (which is what you describe when your foot "splays"
5. lower back pain (to the side of your buttcrack) that comes and goes... generally just an ache, nothing terrible
6. intermittent groin pain (my guess is after running because your adductors will get especially short then)
If this sounds like you...I have plenty of ideas. I think you are not responding to stretching because you are not stretching the muscles passively and also not at the right degree. For example, depending on the way your ilium is pulling you can attempt to do numerous hip flexor stretches for hours and it might not only make zero difference, but it could potentially make it worse in the long run because it's stretching against your hip. If you are attempting the kneeling or standing hip flexor stretch I recommend not doing this.
Send me an e-mail if you'd like to try a few things. I could be wrong with the above assumptions. One thing I would try to do is don't assume you are only externally rotating (which is waht produces the toeing out) when running. Chances are you are ever so slightly toeing out even during normal walking. When walking around your home and you stop in front of a sink or counter or wherever, DON'T move. Look down and assess your feet. Is teh affected hip slightly toeing out? You don't have to be duck-footed. But you'll notice the difference. If so, attempt to slide it in so it's pointing straight. While this might not hurt, does it create a small pressure/tightness somewhere near your pubic bone or groin muscles? Again, shoudln't hurt a lot, but you'll notice your groin area fights this internal rotation. It probably feels more relaxed with your foot towards the side. This is tricky to do without overanalyzing. You can also check yourself if you plop down on the couch or lay down on your back. If it's dramatic enough even your thigh will feel mroe relaxed externally rotated on that side. It will cause more adductor tightness to rotate it back in alignment with the other leg.
E-mail me if you feel you want to discuss some stretches/exercises...