Any ideas as to the removal of stains on enamel?

[Denzil_DC]

6. Good suggestion. Another thought - maybe a steam cleaner,

if the OP has, or can borrow or rent one (perhaps there's other cleaning it would be useful for)?

Depending what's behind those vents, she might have to be careful in giving it a period of warm ventilation afterward to make sure no moisture that had gotten inside would cause an electrical short.

The cleaning product I had in mind above is nastily caustic, but it cleans oven grilles very well without heat, just needing an overnight soak and a hot water rinse and some gentle brushing. OTOH, it's a rotisserie, so it's got built-in heat! Just switch it on for a few minutes, switch it off, then apply the gunk.

Maybe the way to go would be to try a sequence of products, going for non-abrasive ones, from the more innocuous to the more aggressive, and see what might shift it.

Or she could do what the folks who sold me our oven did - not clean it at all, probably on the basis that I was going to give it a damn good clean myself before I let food anywhere near it!