I'd say go to Lowes and spring for two four foot shop lights with a protective metal grid and with the plugs already attached, hang them from chains, install 8 four foot t8's and your table will be as bright as a used car lot. Oh wait, several of us have already given you that proven solution.
Why ask for advice if you are loathe to follow it? The bright and even light will also eliminate all your shadows. Little wonder you complain about brightness. That setup looks like a cave.
If you require another opinion, call: 216 266 2121. It's NELA Park in E. Cleveland, Ohio. The world headquarters for the General Electric Lamp Division.
I worked there for several years, and my Dad for 37 years. Perhaps they are informed enough to meet your needs. Nobody here seems to be able to do that for you.
As proof, look at my avatar. The slight fall off of lumens at the head of the table, is an illusion and is merely tricking the eye due to the Inverse Square Law. That head area is identically bright as is the foot area. Additionally, 8 feet of lamps eliminates shadows since at all points, they are firing light directly down and perpendicular to the playing surface . To exaggerate, you could keep your 4 source setup and put in 150,000 candle power aircraft landing lamps, and they will still give you uneven illumination and shadows since they eminate from four separate and oblique fixtures throwing that light down at an angle. To see this, take a flashlight and shine it on the balls as you walk around your table.