Is 3 yr out too late for mod. Damage to recurrent laryngeal nerve to heal on its own? Is deep ache/muscle spasm after much talk compensatory effort?

Permanent damage. 3 years is well outside the window for spontaneous nerve recovery. Ent surgeon can document vocal cord paralysis and determine if your muscle spasm is related.
Rec. laryngeal nerve. Most injury to that nerve heals within 6 month. The prognosis after that time frame is poor! sore throat and decline in voice quality towards the end of day is due to fatigue of the undamaged contralateral vocal cord. There are surgical treatments to improve your voice. See an ENT doctor.