Pool Table Light with drop ceiling

I am in SE Michigan too so I know there are several good electrical supply houses around. Go to a good one, not a Home Depot, Lowe's, or Menard's. They make a special bracket to do just what you want to do. FWIW, I am not a fan of plastic electrical boxes and have used none in any work I have done on my house. If that box cracks, a wire slips off its connection, or a ground wire comes off of its connection or out of its wire nut, suddenly everything inside of that box is hot. I would much rather have my box and conduit grounded and be sure.

SE Michigan is a big area so I don't know exactly where you are. I grew up in Allen Park but am in Fenton now. There used to be a good place near the corner of Southfield and Fort Street in Lincoln Park called Carter Electric. Where I am there is a good place in Grand Blanc called Winn's Electric. It seems to me I remember there being a Madison Electric somewhere in the Detroit area too. I am working off of memory as my Dad was a licensed electrician but passed away several years ago. Some of those electrical supply houses only wholesale to licensed electricians so you may need to find a buddy to front for you. Check the Yellow Pages or internet.

On the hanging issue, what comes to mind is the bracket that you use to hang a ceiling fan from a suspended ceiling. If it would support a turning ceiling fan it will support your pool table light.

You can get clips that attach to the tracks for drop ceilings, so that you would be able to hang that from it. Otherwise, you are pushing the same wire that holds the tracks, through the drop panel, attached to a joist, so you can hang the light from that.