I ended up using a carving bit for the Dremel to carve around the broken screws, then using needle nose to pull them out. I drilled a 3/8" hole about 3/4" deep. Took a dowel rod and ground several grooves in them (to hold epoxy). I then fit the dowels into each hole, marked them and cut each.
I mixed up 15 minute epoxy and sawdust. Filled the holes and rolled the dowels with epoxy and put them in the hole.
While that was setting up, I wired the light in.
Then I put up the light, leveled it and drilled the dowel rod inserts. I ran sealer around the light. Might add, several layers of sealer.
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