Donna,
That's an extremely impressive summary of your new lamp!
Some scholars have attempted an interpretation of the shoulder decoration on these Hayes Type IIa, produced by stamping poinçons into the damp plaster mould, but I suspect that most of them are simply abstract successors of the more naturalistic shoulder stamps appearing on a few of the earlier Hayes Type I and are merely decorative. The thin concentric circles on the base of both your lamp and the Getty example are a standard feature on Hayes Type IIa from Byzacena in central Tunisia and are unrelated to the shoulder decor.
> the dealer identified it as a deer, but there are no deer in North Africa!
You're forgetting the 'Barbary stag' (Cervus elaphus barbarus), a subspecies of red deer native to Algeria, Tunisia and Morocco. They were presumably far more populous in antiquity and are quite often depicted, typically with large branching antlers, on Roman lamps from North Africa.
It should also be borne in mind that lamps made in North Africa were largely intended for export and their makers did not necessarily restrict iconography to only native fauna.
However, I'm no zoologist but I think you may well be right that the animal with straight short horns on your lamp is more likely to be a species of antelope.
David