http://www.rubylane.com/item/167844-9957/Griswold-Classic-No-501-Singleanything like this one ??
I have an old double burner similar but not as ornate.
The burner on the one in the picture appears to be simply a wavey washer looking thing and I can see where rust would choke it down to almost no flow. Try actually pumping the vinegar thru the gas inlet valve with perhaps a pump up garden sprayer then hit it with the air compresser to dislodge the offending rust. .
Doug help me out on this one......
In one of the pictures the cooktop is upside down and the air bleed opening is shown. Am I correct in that there was a light duty tin piece that slid forward and back to adjust the mix of gas and air.
It is clearly missing in this picture IF there was one ( and I am betting there was ) You might experiment with some duct tape as a temporary test fix in various positions to see if fixing this adjuster will make a difference.
Let us know how it turns out