“I realize they can easily be melted down, but are silver bars marked in any way to distinguish one bar from another?”
Most are...
http://www.tulving.com/bullion/engelhard_silver_bullion_bars.htm
I would posit that very, very few private holders of bars mark down their serial numbers. They are “easy” (not really) to melt down but anyone who does so loses $50-$100 per bar assay charge converting it from a known item (eg; “Englehard 100 oz bar) to an unknown blob or block of silver.
There’s the dollar, the peso, the mark, the ruble, the pound and now “the blob”.