Yeah, if that’s the case I’d tweak the input stage a bit, and also the output stage (make the 470k smaller and the 1k output resistor larger).
Ignoring the input stage for a bit, here’s the VCA core with the OTA and the I-to-V converter:
EDIT: The CV in this drawing is relative to the Iabc input potential, which is two diode drops above the negative supply, not 0 V, so with a 12 V supply the CV in the simplified circuit above is shifted by 10.6 V. The CV input circuitry needs to compensate for this in some way, see e.g. here.
R1 and R2 divide the signal from the input stage (note that there are two R2s, both resistors should have the same value), R3 converts the shifted CV to a current Iabc that controls the gain, and R4 converts the 13700’s output current to a voltage. Putting all the equations together and simplifying somewhat, you get:
Vout = Vin × CV × 19.2 × R2 × R4 / (R1 × R3 + R2 × R3)
or for a given Iabc:
Vout = Vin × Iabc × 19.2 × R2 × R4 / (R1 + R2)
To increase the output level for a given Vin and CV, you can increase R2 or R4, or decrease R1 or R3.
(There are some additional constraints here; the input level (Vin × R2 / (R1 + R2)) needs to stay under 100 mVpp and the control current (CV / R3) needs to stay well below 2 mA, and (less likely) if you make R4 too large the output stage will clip).
Putting in the values from your current design, the VCA gain is
CV × 19.2 × 1000 × 1000/(39000 × 47000 + 1000 × 47000) = CV × 0.01
so with a 10× input stage, you need a 10 V CV to get 1:1 at max volume (assuming my math is correct, that is 
).
You could go with a 1× input stage (two 100k resistors); that’ll handle 4 Vpp at max volume (Kosmos spec says audio is 10 Vpp, occasionally 20 Vpp, but you can use the volume control to deal with that), and then increase the output resistors to at least 10k, maybe a bit more depending on what CV levels you plan to use.