Unless you are working in a NASA grade "clean" room, no matter what method you use you will almost never get every single dust spot. Even if you do, by the time you put a lens back on the camera, more dust has probably made its way into the mirror box of your camera and some of it may eventually find its way onto the surface of the filter stack in front of the sensor. The front of the filter stack is what is cleaned when we use an air blower, swabs, etc. on our camera's 'sensor'. So the point of sensor cleaning is not so much to get a 'perfect', dust free result as much as it is to reduce the amount and influence of dust on your images to a minimum achievable level.

When I clean one of my sensors I take test images after each pass with a swab. After early attempts to get every single spot and going through several swabs, similar to what you relate in the question, I've learned to 'quit while ahead' even if there are still a few light dust spots remaining. The next pass at that point may well result in more dust spots showing than remained after the previous attempt.

Before I use the first swab, I'll often try several clean/test cycles with the air blower. If none of the spots are staying in the same location on the sensor, I won't even use a swab. I'll just continue to use an air blower until I get a test image that gives a result that reaches the level of 'as good as can be expected'.

Corners are always the most difficult to clean with a wet swab. It takes a bit of practice to learn how to use the edges of a swab to clear out each corner by slightly rotating the stem of the swab back and forth at the end of a pass. But based on my experience, doing it yourself will never result in a perfect result with zero dust. Based on the experience of others I've talked with, neither will dropping the camera off at a local camera store and paying them for cleaning the sensor.

I've never shipped a camera to a factory service center to have a sensor cleaned. Maybe some of them have methods that can get a near perfect result. The cleaner environment in which they work on cameras and lenses certainly can't hurt.