It sounds like an earth loop and/or mains inducted noise via the HDMI cable from the projector.
How was the turntable separate earth cable connected?
How long is the HDMI cable to the projector?
Is a power cable run with, or near the HDMI cable to the projector?
Have you tried connecting a separate earth cable between the amp and the sub?
Have you tried a different HDMI cable to the projector?
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