I wouldn't worry too much about the paint. It's not going to do any harm and won't make any kind of mess. Burning off in the areas I mentioned is considered common. That would also happen with any paint applied on a new engine direct from the factory. They wouldn't be using any special high temp paint. As far as the heads are concerned, they're going to be mostly covered by air shrouds anyway, along with the cyls, aren't they? At least they are on my 4 cyl Wisconsin VE4D. I wouldn't try and apply any paint over the existing - that could make a mess with wrinkling of the film, especially if it's a lacquer over enamel. A proper re-paint would involve completely stripping the existing paint.
Good luck in getting it running properly. Is that a hydraulic pump it's driving? Does it go in a skid-steer?