I have a built-in FireMagic Regal II bbq. The thing is rather large and it's all stainless steel. To clean the hood, I typically use furniture spray (it's oil based and actually works well). The front of the hood doesn't get too many stains.

However, the front plate (w/controls) has black grease drips. I can easily remove the front plate if necessary. The furnuture polish doesn't work well on that for removing stains, etc.

I need suggestions for making that front plate super shiny w/out using an abrasive. I live in Southern Californial. Thanks.
I've purposely kept this question open because there were so many good ideas. I did try the vinegar idea. It did indeed clean well if I applied a lot of elbow grease. However, if you've seen the size of my bbq then I could be spending hours and hours. I'll keep trying everyone's suggestions. Thank you for the great answers.