I interpreted this as not 1/2" wide but 1/2" thick, by say 1" or 1
1/2"wide...

Am I missing something here or are you just Trolling: it doesn't seem
possible, to me, to put a 5/8" [0.625"] hole (of any shape) in a 4/8"
[0.500"] wide piece of metal - the hole would extend 1/16" [0.0625"]
outside the metal on each side.

Either use a wider rail - 3/4" [0.0750"] - or a thinner picket - 3/8"
[0.375"} - or simply cut the rail into pieces (whose length is defined by
the picket spacing) and weld them between the pickets.