You must have something like the one in the photo below. Often called a pancake or dome light. I don't think you'll find an LED "bulb" that you can install to get multi-level lighting or another similar pancake light.
If you are the handy type, here's what I would suggest. If you remove one of these pancake lights, you'll find a roughly cut hole around 1" or so and up to 8 screw holes. Then buy a few round LED "puck" lights as in the next two photos. The ones in the photos are ones I recently bought on ebay (around $10 each). They have plastic lenses and are very light. I bought 4.5" diameter ones.
Then install the new lights where the existing holes are. I would install 3 lights and that way you can wire up switches so you get 1/3, 2/3 or all on using 2 switches (1 sw. controls 1 light, 2nd switch controls 2 lights. You could mount the new switches on the ceiling near the new lights. The pancake light there now will have unswitched 12 volts DC.
With the recessed puck lights, you'll get less glare and they will be visually more appealing. Luan plywood is easy to cut with a utility knife. If you were to install the puck lights, you could perhaps install 4 total - 2 to replace the pancake light and one farther back from the centerline of the table, closer to the table edge.
Another option would be to replace the pancake light with something like the last photo which is 12 volts. If you can find one with two or more lamps in it, you can get multi-level lighting. The one in the pic is halogen though and you'd have to get some LED lights (ebay) and you could even add another LED array/lamp or 2. You'd have to install a switch somewhere.


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