The oxygen flow rate is set by adjusting the air pressure (using a pressure regulator)on a pneumatically controlled diaphragm valve which moves a sliding gate in the oxygen supply line.
With only 6 psi of differential, yes, you may have trouble controlling the oxygen flow due to several factors.
What is the liquid head developed at the injection lance (how deep is the end of the pipe in the liquid metal pool, and how much pressure is then required for the oxygen to flow)?  If the depth of the tube varies, your flow and pressure will/must vary too.
How are you controlling the opening of the butterfly valve (or do you just modulate between full closed and full open?)  Do you know the Cv of the valve vs. opening percentage?  If yes, then you need to control or measure the differential pressure across the valve as well as the upstream pressure.  You may have better luck with a fixed orifice in the line, a shut-off valve downstream of that, and a pressure regulator feeding the orifice.

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