"two different camps within the same park" they are actually just different private reserve names for legacy reasons of land ownership, but they are all unfenced and contiguous with the National Park. The difference is more about vegetation and landscape between different areas, which relates to permanent or seasonal water (either watercourses or waterholes) in the traversing area, and the vegetation types around the lodge you choose.
If you are happy paying for bush flight transfers between the lodges then going from a southern Sabi Sand lodge to Timbavati (or Manyaleti or Klaserie) is easy, whereas road transfers are a pain. I am aware you can fly to Phinda. You could also consider Tembe as an alternative that won't break the bank and is owned and managed by the community. In the far north of Kruger both Pafuri Camp and The Outpost get amazing reviews. I don't know what the transfer is like, so with only 5-6 days a main consideration should be the practicality and cost of moving such large distances.
Sorry I can't help with recommendations of private reserve lodges (we prefer to spend less and go more often)! Enjoy the planning and the holiday, I am sure it will be incredible.