Our most experienced embedded engineer, FredM, who unfortunately passed away too early, always said that a PLL in a theremin was an overkill.
What Bob Moog did in the series 91 theremins could be of interest for you: He started from a 2.8MHz crystal oscillator, did some uneven or prime number dividing to obtain two reference frequencies where none would intersect withe the harmonics of each other. These square signals were fed via small (22pF) capacitors into parallel resonant circuits with relatively small L and big C (and good old variable capacitors for tuning) to which the antennas were connected through linearization coils as in a classic heterodyning theremin.
Analog phase comparators were used between the original and the dephased signal (before and after the small series capacitor) to obtain the analog pitch and volume CVs. The volume CV went to a LM13700 VCA and the pitch CV controlled another LM13700 as an audio oscillator, outputting a triangle wave which went then through the classic Moog style non-linear filter wave shaping.