The possibility of having the anode and screen at different voltages was covered in the original Hafler and Keroes ultralinear article, and in the associate patent. It was done by having a separate transformer winding for the screen grid.
In fact, it looks as if this were the primary approach to ultralinear, with the use of a transformer tap for the screen grid viewed as being a simplified approach that incurred the need for a common HT voltage.
The original Audio Engineering article and the patent are attached.
Cheers,