I’m a novice cook and mostly use nonstick pans for ease of clean up. Would I get better browning with stainless steel? I’m imagining scrubbing stuck on food off the pan... What are some general rules about things that are better cooked in stainless vs non stick. Are there certain foods to avoid in stainless (to avoid ruining the pan or scrubbing all day). 
If you can find a mesh cover large enough to go over the top that's certainly an option, you need to work out a way to keep it in place, you don't want it sliding around on you. Meat will stick, lifting the meat off when it's stuck will cause shifting if there's nothing holding it in space. Perhaps an easier option would be to get long metal kebab skewers instead of a mesh or slatted grill. If these are long enough they could go the long way across, or they could be placed at an angle from the rim on one side to the body inside. This would give you a lot of flexibility to control the amount of heat each piece of food gets. One solution I've often used for campfire cooking is to place a cast iron frying pan straight on the coals, that would work just fine on your fire pit as well. 