Annie it does seem like you have a very uncommon presentation.
I am just thinking if maybe seeing as you have a had all these tests in the lower leg nerves such as tibial nerves etc, and found no answer, maybe the problem is more proxmial with radiating/referred symptoms.
Can you explain what you mean with neutral int.ext rotation, do u mean just no rotation and in 90 degree flex.
When you flex your left hip past 90 degree , besides stiffness do you have any neural pain. Is the stiffness there at the same point when passively moved.
Is there any one movement that you have do, any palpation that you can do, or during any tests with chiro, did u feel the pins and needles, burning come on immediately.
My reasoning behind why it may be more proxmial is that in relation to Dr Damiens comment about your back. It'd be interesting to assess your lumbar spine. The femoral nerve originates at L2-L4 and is the main nerve which innervates the anterior thigh muscles. Any compression ( usually found with idiopathic femoral neuropathy) may cause weakness in the hip flexors. The neural pain may orginate in the groin and travel through the medial aspect of the leg proximally but can radiate through the saphenous nerve down to the region where you are experiencing problems. I have not read of any instances where the problem from a compression proxmially presents more distally but i have seen stranger things happen before!
In addition if you have any stiffness or tightness or muscles shortening which may be causing any nerve compression, the yoga and stretching may be giving you short term benefit by lengthening the muscle so i wouldnt expect it to cause you trouble. The fact you cannot run also indicates that immediate compressive forces cause you problems which goes in conjuction with my reasoning.
I feel that from what you have said and from the information ive read, you have had so many inconclusive investigations, id definately look closely at the femoral nerve from origin along its root and to see if any tests may provoke your symptoms. I feel that if you have any compression on the femoral nerve in your lower back or via musculature on the nerve root it may produce similar symptoms to what you have said, especially as you are now saying that you have pain in your groin too.
Like i said this is purely my own idea and i hope ive reasoned my thoughts well. Im not a narrowed minded practioner at all so would love to see other physio's inputs so we can get a clear answer!
Keep me posted