I'd try and spot any particular causes to why you're not sounding as clean as you'd like, then basically troubleshoot the problem. Is your finger disrupting another string in motion? Is it buzzing? Sympathetic resonance from other strings? While you don't have palm muting, you can still make use of left hand control to dampen strings, keep that in mind.
How I practice clean transitions, is I'll play a chord, and before I move to another position I'll quite literally relax my hand and fingers staying in contact with the strings, and then move. While this process is like three steps (play > relax > shift position), the goal with practice practicing is to reduce the duration of this process to the point where it's like one flowing movement. This has helped me get rid of squeaks and buzzes, but also adds a relaxed dynamic to my playing, more controlled, it's audibly noticeable. Hope this helps.