Reporting my results. The steel wool did the trick and the varnish was very forgiving. It must be very hard varnish. A friend of mine made the fiddle and I decided not to tell him what I did. He might read this and find out though. Who knows? I can now see the wood and it still has a nice luster but without the glare. I'm so happy!
I tried both dry and oiled steel wool and I think the oiled worked better. The dry might have scratched it a little. I buffed it again with oil and tripoli. Then put new strings, new bridge, and played for a couple of hours and enjoyed it more than I ever had before.