Okay the problem is twofold the bright overhead non-directional light!
this causes tv to be hard to see due to ambient light spread !
best to move tv and put in a proper diamond light at right height
or if cannot install 4 led daylight hi hat recessed lights on dimmers in drop ceiling spaced over table!
they are cheap to run and buy use 11watts with a 65 watt output rating ,
Home Depot here for less than $20. plus new work light rough in can $5.00
cool to touch, easy to install, if needed, you could add 2 more easy?
nice thing they shine light down so very little reflection on tv for viewing !
another hint there are available recessed led light trims that fit in a 4" standard octagon electrical box for low height restrictions in ceilings!
love the daylight easy on eyes!
fyi led panels in ceiling will not be best, as there will still be light spill reflecting on tv, these lights are not downlights but area lights ,same as any overhead non directional fluorescent lights!
Yep retired Master Electrical licensed contractor who works pt at HD