I’d guess that it’s because the clutch has worn and is now slipping a little rather than moving linearly, so that whenever you’re getting pedal bob and thus chain growth it’s making said noise. Perhaps rather than loosening the clutch actually try tightening it a little bit, to try and counteract the wear.
As a side note I’ve just got a clutch mech and didn’t realise what a difference to shifting it would make when it’s on, obvious in hindsight I suppose but it doesn’t exactly engender me to running with it on, I like my smooth shifting. Good before a “gnar” run though.