Kevin,
I'm looking at 1957 and 1958 GE literature, and don't find your exact range in either publication. However, as has been noted here many times before, GE had more variations than "Carter has pills". I still say your range is not a 1959 because GE used a black component on the console and they introduced a "deluxe" clock/timer that looked different from the past 2 years. The J-304 was the TOL 30" range, complete with keyboard controls and a meat thermometer and a plug-in griddle. The '57 suffix was 'P', the '58 suffix was 'R'. The next 30" range in the line-up was a J-303, but it did not have the pedestals and the glass panel at the rear of the cooking surface. Clearly, your model would be something between a 304 and a 303, but I do not have anything that shows it or references a model number. It would be interesting if you could find a model number (possibly on the lower front, concealed by the storage drawer), it should tell you/us more.
Lawrence