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Your original suspicion about the chips may be correct. The data sheet for the CD4046 shows a typical frequency limit for this chip of 600 to 800 kHz at 5 volts and 1.2 MHz for 10 volts. The frequencies of the upper broadcast band will be higher than the IC is specified to operate.
I know that the 74HC series chips works but the supply is limited to 5 volts. Unfortunately, the next step appears to be to replace your ICs.