I've tried using just about everything to clean my old, original, cloudy stainless steel. Never Dull worked okay, but you could steel see the water stains and cloudyness. I was finally able to get NOS looking results by doing the following:
Got myself 2 (creates a wider buffing surface) medium Mibro buffing wheels and Mibro's #3 and #6 polishing compound. Since I'm restoring the my car right now, all the drip and reveal molding is off the car, so what better time to do it?
I installed the 2 buffing wheels side by side on my bench grinder, as stated above, this give you a wider buffing surface.
I start with the #3 compound which is more of a cleaner that is safe enough for stainless steel. I coated the buffing wheels liberally with the compound and slid the molding back and forth all the while appling LIGHT pressure to the wheel-let the buffer and the compound do all the work. Take your time and be careful not to let your molding slip out of your hand and get tangled in your bench grinder! After buffing with the #3 compound, wipe the piece down removing most of compound off the piece.
Now you are ready to move on the compound # 6. This is what really brings out the shine! Again, coat the the wheel liberally with # 6 compound. Slide your molding against the wheel remembering to apply only light pressure. Once you have buffed the whole piece, use a polishing towel to remove the excess compound and stand back and enjoy the brightness of your NOS looking stainless!
Remember to take your time and be careful not to let your molding slip out of your hands!
Oh yeah, wear old pants too as the compound gets all over your pants.
I guy I know paid 200 dollars to have his molding polished for his Chevelle. I got all the stuff I needed for this project at Lowes for about 20 dollars and it took me about 3 hours total to do the front reveal molding and drip molding.
Good luck!