I can't respond to the physics but I can tell you to use the 74HCT4046 or better an 'old' signetics NE561 or 2.
The CD4046.. even the "BE" versons had VCO's that had stability issues because VCO power supply. The 5V HCT4046 had a better more stable VCO but If I could find them I'd use NE/SE561's.
Back in the 60's I was making SCA decoders (Secondary Audio Channel) and the NE 561'a or NE567's with some extra effort were more stable and easier to use then CD4046's.
Bob