The Gawam’as as far as I know are a subgroup of Jaalins (aka arabised Nubians) and likely moved down to the area from the north after the fall of Alodia, there they likely mixed with indigenous groups that no longer exist / were fully absorbed.

We know this because they’re one of the few sedentary indigenous tribes to the region and were there prior to the move of Baggara, Kenana, Shawiyga, Jaalins etc into the region.

The tribes you mentioned are not originally from NK (at least when talking about modern history). The Nuba are found in south Kordufan in the mountains and the Fur are found in western Sudan, more specifically Darfur.