There are three reasons the paint might not be approved for food surfaces:
1. the chemistry of the paint remains toxic after curing (like mold-resistant paints)
2. the pigments might be toxic (many exterior grade paints)
3. Nobody bothered to test it for toxicity because of cost and liability, so it's 'disclaimer labeled' against the use.
Unless you're actually planning on eating food that has sat on the painted surface for a while, its residual toxicity after curing should be of very little concern.
I recommend that you use a burner cover of some kind if your cooktop is going to be a food prep surface - ideally something like a food-grade cutting board. If you promise not to use the stove itself as a cutting board or salad bowl, the toxicity questions are much more easily managed.
The one thing I would positively recommend is to cure the paint in an oven (or with a heat gun - hard to do evenly) after painting
. The major toxic element in most paints are fumes given off during the curing process. On a nice day with windows
open, Paint the stove top, let it sit for a few hours at room temperature, then pop it in a ~150 F oven to cure for an hour or two. In summer you can just leave something like this sitting out on an asphalt driveway and it'll get hot enough to cure.
The idea is to get the stove top as hot as it is likely to get in normal use in a well ventilated area to encourage it to outgas somewhere that isn't your trailer. The gases given off by curing metal paints tend not to be good for living things and are a big part of why EPA encouraged water-based finishes for new cars starting in the '90s.
As a rule: if it smells like curing paint, you probably don't want to be shut up in a poorly ventilated small space with it.