Pretty sure food grade is 316

This is the delima. The 300 series stainlesses seem to be prone to heat cycle warpage and are inherently "soft" ie. ductile. My semi-uneducated SWAG leads me to think that a 410 would be the best choice to start the experiment (price wise). If money is no object, 440C...Now that's some tough stuff even fully annealed.
When I was making knives, used this stuff. ATS 34 (1.25% carbon). It has a 2100F quench and 900f draw temp, so a grill fabricated from this should hold up really well.

I have 18" diameter replacement grates for my Big Green Eggs that are 304, and they work great. These were part of a special production run, so I'm guessing the manufacturer had a jig to minimize warpage during fabrication.  They look like a standard grill grate for a Weber kettle, only the rod is slightly heavier and there are two stiffeners under the main rods.   When making my own BBQ accessories with 304 (in 1/8", 3/16" and 1/4" rod) warpage is an issue, so balancing the heat and making small TIG welds is mandatory.

For your application, there is one thiing you might look into..... custom grill grates.  They are spendy up front.  These guys come to mind as they are members of one of the BBQ Forums I hang out on.  I do know they work in stainless, even though I did not see mention of it on their site.

http://www.huntingdoncocustoms.com/

~thirdeye~

400 series will rust 300 series will last for ever at the low temp of a grill also the least oxidation at high temp's

316L is food grade stainless I use 1/4 inch round stock and it works well so far.