If you look at pictures on Houzz of ping pong tables, almost all of the rooms have pot lights. If you place them on a dimmer and turn them up very high when playing and have them strategically placed as well, maybe you could avoid shadows.

This is with 9 very bright recessed lights. You can still see shadows.

It's not so much shadows as areas with brighter lights that you want to avoid here. A bigger diffused light right over the table would work better than individual pot lights similar to those old boxed fluorescent lights they used to put in kitchens. Maybe a DIY custom diffuser box over the existing pot lights might do the trick?