Sorry about the delayed response.
Your case is a complicated one. The main differential, in general, is Peripheral nerve hyperexcitability (PNH) which entails a spectrum of diseases or may be labeled as cramp fascicular syndrome or myotonic disorder and metabolic myopathy.
The basic mechanisms of each diagnoses are different. In PNH, auto immunity must be ruled out whereas in metabolic myopathy enzyme deficiencies should be ruled out.
Key diagnostic tests include EMG, muscle biopsy, CPK,
CBC. Perhaps electrolyte panel. (a muscle biopsy which is a minor in-office procedure certainly can be done by a general surgeon and depending on experience GP may do one)
Also, for metabolic myopathy a test called forearm ischemia exercise test can be done. This messures the levels of lactic acid and ammonia in the blood before and after exercise to see if the muscles are able to use glucose and fats as their energy source. In metabolic myopathy, the problem is the body's inability to use either glucose or fat for motor activation.
The treatment for PNH includes anti convulsants or immune suppressants... therefore neurology or rheumatology respectively are appropriate.
Seeing that rheumatology, endocrinology, and neurology are already involved, it is reasonable to expect the family physician to serve a main person to bring all the test results into a collective picture and attempt to coordinate care.
Again the key question is: Is this metabolic myopathy (enzyme deficiency) or is it an autoimmune problem.
ps Let us know how things go.