Dear WannaRun
Reading what you have written so far my thoughts are you have issues in your left hip.
My thoughts are as follows an imbalance involving the internal and external rotators. Some degree of rotation seem to aggravate your groin pain...
It is possible that you have either an internal/ externally rotated hip which is anteriorly displaced so that everytime you do a twisting motion you have an anterior compression in the hip...
This rotation could happen when squeezing a ball in between your thighs...
Although a lumbar spine issue could be also the cause...
do you get the pain on hip flexion, extension?
I do not know the details of your assessment with your physio or sports doctor but what i would suggest is testing the strength and comparison length of your hip external and internal rotators...
the fact that its painful in the mornings now suggests some form of arthritis, which would support the theory of a hip muscle imbalance...
It would be helpful to know the details of how this groin problem started...
In the interim joint mobilization of the hip, prone kneeling and rocking forward and back within painless limits can be trialled
what did theMRI scan report say?