Inverter ringing on high side : how to minimize it?
We're seeing quite a lot of ringing on the high-side mosfets, we scope
it with the negative of the oscilloscope on the phase output and the
positive at the +VDC

That'll be your problem - the DS1054 doesn't have differential inputs and you are connecting the &quot;grounded scope input&quot; to the hot output line in your push-pull converter. Thus you are adding a whole lot of ground to the hot output line and usually that means shorting things out. However, in your situation, I expect the output is floating but, you are still adding nano farads of capacitance to a fast  switching line and causing parasitic circuit inductances to ring.
Never do this unless you have proper differential input probes and, at $400 dollars, the DS1054 is unlikely to have them.

Could it be a measurement effect of us not scoping it correctly?

I believe so.