You can remove the rust using ZUD found in most grocery stores... I bought mine at Safeway. It's a powder like Comet. I also use it in my stainless steel sink. Because the metal is pitted, the rust will come back. But Zud and a little elbow grease is cheap in comparison to replacement. If it was in my home, I might replace the stove just because I didn't care the way it looked. But FOR ME, this is a trailer, it looks perfectly acceptable and more importantly, works just fine.
Your mileage may vary.
Ten Forward - 2014 Escape 5.0 TA
Double Yolk - 1988 16' Scamp Deluxe