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Coupla things come to mind, I think you are right re. string type,…that is one piece of the puzzle. I also think you are right regarding your chord shape moving and leaving enough pressure on the strings for that squeak sound to become noticable. Especially noticeable with bar chords. There is also a finger texture component as well. The harder my callouses get the less sound they make but again that is when they are on the tips. There is also a speed of transition component. The shorter your transition the less time for the string to squeak. Have you experimented with keeping pressure on your chord while you slide. It gives that slight feel of chromatic sliding but may be preferable to the squeak? It takes some time but you can develop the touch to move up and down the fretboard without contacting the strings. Tension management is fairly critical as you develop that touch accuracy.
Hope you get to a good solution.