I have a set of Craftsman bolt extractors that are spiral hex that grab a rounded head as you turn it to loosen it. They might work on rusted heads. Here's a link to various similar extractors. Link

If you want to try a metric socket, I would try a 14 mm first, as 13 is REALLY close to 1/2 inch (0.512"). 14mm is 0.5512" while 9/16 is 0.5625". Whatever you try would definitely have to be 6-point rather than 12 point.

Kevin
1951 Chevy 3100 work truck
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1929 Ford pickup restored from the ground up. | 1929 Ford Special Coupe (First car)
Busting rust since the mid-60's
If you're smart enough to take it apart, you darn well better be smart enough to put it back together.