Specific live recording conditions...

I was offered a job to film conferences in a movie theater.

I have usable cameras (studio 4Kpro MFT and Ursa 4k8g2 EF). I am considering a camera at the back of the theater and a camera dedicated to the speaker.

My problem concerns lighting and the choice of lenses. Theather can hold 200 people. The speaker with his microphone stand is installed on the left of the screen.
I have to light the speaker without creating a shadow on the screen.
As it is a highly reflective cinema screen, the slightest stray light is visible. I was thinking of creating a cross beam from two 3,50m T-bars on each side of the stage...
The speaker's face should be visible with regular lighting on both sides. Follow spots are not usable and speaker want to see public.

T2 aperture seems to be a minimum...

All advice is welcome.

I would also check the scan rate of the projector to avoid rolling bars.

I made some tests today with your warning in mind. They use 4K DCP and I didn't noticed a problem recording also in 4Kp50. But when a customer will use his laptop, it may be more tricky.

I tryed also some redhead lights but I did not succeed : bad lighting of speaker face.

I have two weeks to try or decline...