Stainless plate for gas barbecues would have two special service issues that I can see: heat exposure and chloride exposure.
Chloride ion is problematic for most stainless steels, which is why marine and FOOD SERVICE applications often specify special stainlesses. Whether there is enough food exposure depends I would suppose on where in the product the steel is being used. Barbecue sauce is typically loaded with salt, and that is your chloride source.
Similarly, heat exposure would not be the whole barbecue but only certain areas.
I am presuming that appearance is an issue, you want something that will continue to look good.
From Stainless Steel Handbook, p7: "... the low alloy steels such as Type 410,
12% chromium, being less corrosion resistant that those steels having higher alloy content such as Types 316, 317 or 446. This variation in corrosion resistance appears to be related to the amount of chromium contained in the steel, and the resistance can be improved by the addition of nickel or molybdenum."
It is worth noting that standard flatware stainless is typically 18/8 at least
18% chromium and 8% nickel. The addition of nickel improves the resistance to chloride ions. Some cookware uses 18/10.
From Stainless Steel Handbook, p7, further on: "Consider the use of a steel for resistance to the corrosive elements in an industrial atmosphere. Type 410 or any of the 122% chromium steels would develop a superficial rust after several weeks' exposure. The film formed acts as a barrier to further corrosive action, but the resultant part is objectionable from an appearance standpoint. Type 430, 17% chromium, will take several months to form the superficial rust film. The additionm however, of 8% nickel to Type 430 produces a steel, Types 301, 302, or 304, which will not form a rust film and will remain free of corrsosive deposits. In some atmospheres even Types 302 or 304 are not satisfactory, particularly coastal installations, and a steel having higher corrosion resistance such as Type 316 must be used."
Type 301 is only 17/7, whereas 302 is 18/8. 302 is the minimum likely to work well, and if it does not suffice, then 302B, 316 or 317 or 314 would be canditates. However, if 302 does not suffice, 401 will be horrible. 304 is very similar to 302B, (not quite as much silicon) so I think that if you've had issues with that, you may need to upscale to 316 or similar. However, 304 and 302B have better heat resistance. 302B should be better than 304 for most high temp applications.
Is there any patterning to the corrosion that would correlate to either heat exposure, food juice exposure or both?
Another thing to consider is that stainless steels form a surface passivation layer which protects them. The presence of small amounts of certains things in that surface can seriously degrade it. Some people recommend hot nitric acid treatments to passivate the surface after cleaning and degreasing. Such treatments may allow you to use steels that would not suffice without the treatments. I suggest you get the advice of a real, honest to G-d metallurgist to help with your steel selection. Otherwise you will likely get a grade that is more than needed, with corresponding high cost.