I don't actually think the Naza algorithm is basically a PID one.
I write PID code as part of my work, and it is very common to use alternatives. PID is a 'starting point', but often other variants are better, simpler to code, and giving better control. I think the Naza algorithm actually behaves as if it is a significantly modified algorithm, with some self correction. The second set of gains certainly don't behave as if they are the I term, noticeably affecting the instantaneous responses. They may well in fact be affecting an averaging factor, on the readings, rather than the actual loop control....
My own 'suggestion' for setup is:
1) Fix all terms at 100%.
2) Make the basic pitch, and roll slave to your pot. Adjust your pot with the assistant, so you know where the 100% point is. Start with the pot set here. Do this for each adjustment when using the pot. Now, do a flight and tweak these to get good control. You are looking for increasing the value till when you make a movement the copter wobbles quickly for a moment, then just coming back till this stops. Land, read the values, using the assistant, and fix these.
3) Now set the altitude to the pot. Try flying again. This one is harder, the responses are less immediate. One thing to test is how it lands on auto, with a battery failure. If the altitude gain is low, it'll drop fast. Set it higher, and the rate of descent goes down. However go to high, and it can 'hunt' when trying to hold altitude. Ideally as with the other gains as high as useable before this hunting occurs. Like this the descent on a battery fail landing is a smooth steady one....
4) Now fix this gain, and put the pot onto the attitude terms. Again set these.
See how it flies.
If you are still unhappy, go round again, starting from the points you now have. There is a little interaction between the settings, which can make this necessary. Particularly a mode that feels good in Atti, can tend to hunt in GPS.
On the modes, the 'Basic'; position, doesn't use the correction algorithm. It behaves like a traditional simpler flight controller, limiting control rates, and trying to ensure that 'centre stick' is basically equal motor outputs, but leaving it up to you to correct errors.
The Atti mode involves the full algorithms, to try to limit the maximum yaw, pitch, and roll that the model can exhibit, and bring it back to level flight when the sticks are released, but it will slowly drift, since it is dependant on detecting movement (like you trying to keep a boat in one position in the centre of a lake at night - there will be slow drift as unexpected things like currents slowly move you).
The GPS adds an awareness of actual 'position', but with relatively low accuracy (few feet), allowing the drift to be much reduced.
Best Wishes