Gar42,
When neural irritating events take place , leading to altered sensations, it is your brain that feels the pain and other sensations, exactly the same as when a local event takes place, where it is nerves that produce information interpreted by your brain. It will not be possible to interpret the difference between these on the basis of subjective analysis of the sensations alone.
You sound so wonderfully confident about your current treatment regime even though the balance of your likely referred events are still present ( hams , gluts, calves ). while your therapist deals with the lumbar spine with exercise stretch and , as you say ROM . It may take you a long time to realise the kind of effect that ten minutes of Continuous Mobilisation will produce. These kinds of referred events are routinely turned off in my own practice , by either myself or any of my experienced students , in ten to fifteen minutes.
It is not unusual to have L3 and L4 referred events to include burning sensations , along with twitching, itching, cold , heavy, tight etc etc etc , that is why they are called altered sensations. Pain not responding to local treatments are the most obvious among other signals of the common thread of somatic referred events of which I speak. No rocket science or further investigations required , just a shift of emphasis and a willingness to see your issue as a temporary nerve irritation , rather than a mysterious local ailment . Unfortunately it does appear that your therapist is not skilled in local passsive Wikipedia reference-linkfacet joint movement therapies. Find one ,they are out there .