I have a couple of ideas, but I'm no lighting professional, so . . .
1) Contact some of the people who put on professional events that are televised. Those tables are bright and they don't have hanging lights over them. If you are going to video shots done on this table their advice will be particularly valuable. Make sure you get the lighting guy, as others may say they know what you need, but might not.
2) You could build a mechanism to raise and lower an overhead light into/out of position, so it would be in optimal position when you're playing, and raised up to the ceiling when you're not.
3) The light meter advice was excellent, as it gives you and your lighting people something objective to work with. Remember to take readings from different spots on the table.
4) Light from many sources vs from only a few will help a lot with the shadows problem under the rails. Softer lighting will probably help with the ball shadows, as was previously mentioned. Along this line, there are many new high intensity LEDs out now that you might be able to use. Each would throw way too little light, but with lots of them you may get exactly what you want. They won't be cheap, but they throw minimal heat and use minimal electricity. And they last a very long time too.
5) As you no doubt have thought already, this will be a PITA to fix if you don't get it right the first time. Maybe some of the pool hall owners here on AZ who put on pro tournaments can give you some tips and/or put you in touch with someone who can help.
Best of luck to you with your lighting project. I've enjoyed your videos tremendously. Hope I've been helpful.