What I would do next is to tune in the radio's VCO, the output from the PLL that sets your channel frequency.
If you set the Galaxy to channel 20, the VCO frequency should be 16.510 MHz. Tune in this signal. Should be able to "sniff" it near the PLL chip, or near the front-facing end of the transmitter mixer chip. Either USB or LSB will work fine on the external "sniffer" receiver. Tune it a steady tone. Turn the Galaxy's clarifier and you'll hear the pitch rise and fall in step with it. If you don't hear that, you're not listening to the correct internal signal from the radio.
Key the mike in a SSB mode and modulate the Galaxy. See if you can hear any "warble" in the pitch of the carrier's tone in the receiver.
This is one of the most-common roots of garbled SSB transmit audio,
But not the only one, by far. No point trying to fix a 'warble' problem if it's not there to start with.
If the tone in your sniffer receiver stays steady when the Galaxy is modulated in SSB transmit, your problem lies elsewhere in the radio.
I can think of four specific different kinds of distortion that we see in sideband transmitters. Warble is only one of them.
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