Nozzle is scraping along as it moves around during print  

Nozzle is scraping along as it moves around during print

So I'll preempt this with the fact that I am using Cura, tho the settings shouldn't be that different.

I've had an issue during the last month where the nozzle will scrape along the support and model as it's moving around. You can clearly hear it as it sounds like a bad harp during printing. This has the effect that if I use tree support, they're just knocked over, and with normal support the prints will just be knocked off during the transition from support to actual model.

I know what the symptom is, but I don't know what I should be adjusting to fix it. I've tried several things which honestly just sounds unhealthy. I've turned the flow rate down to 80%, and A: It's still not working, and B: The prints looks like absolute shit. I've also turned down the Support Z-distance to zero in hopes of having the the model be stuck to the support a little bit better, but it still gets knocked off. And I've turned support overhang angle down to 25% just to make more of it so it doesn't break. I've also gone through the various calibration steps several times.

Anyone has any idea what the root cause could be and how I could fix it? I've been at this for a month now, wasting several kilos of filament in the process, and I've had absolutely no progress.