Hawthorne Stereo in Seattle has a Linn Majik Integrated (Black Square Version) for under $600 that would work with the Ninkas & Katans. Hawthorne also has a Rega Brio integrated that would also work.
The owner of Hawthorne likes to steer people towards Naim. In that regard, I don't think a Nait 5i pushes out enough power for the Ninkas, but it would work with Katans.
If you're a devout Linnie and able to flex a bit, have you considered getting a Linn Kairn or Wakonda Pre and matching it with a Linn LK140? They are not the easiest separates to find, but they are out there within your price-point.
I'd also avoid the Linn Klout due to the age factor. They tend to run hot and would likely need to be re-capped in short order.
The owner of Hawthorne likes to steer people towards Naim. In that regard, I don't think a Nait 5i pushes out enough power for the Ninkas, but it would work with Katans.
If you're a devout Linnie and able to flex a bit, have you considered getting a Linn Kairn or Wakonda Pre and matching it with a Linn LK140? They are not the easiest separates to find, but they are out there within your price-point.
I'd also avoid the Linn Klout due to the age factor. They tend to run hot and would likely need to be re-capped in short order.