Been flying for a year, 165 hours and still rely on that ball to tell me if I am coordinated.
I don't yet have a sense that I am slipping or skidding based on feel.
When I am putting around the pattern, I am looking at the turn coordinator and correcting after the fact.
Any way to help gain that sense of skidding/slipping so I am not correcting a problem but integrating the corrections into my flying?
I don't think there really is. The idea that one can accurately sense slips and skids is just an extension of the fallacy around 'flying by the seat of your pants'.
Glider pilots are obsessed by coordinated flight because it's efficient and because the ships require lot's of control input to remain coordinated. They are always turning in lift, lift is usually turbulent, the wings are long, adverse yaw is great and there's a lot of 'inertia' around the roll and yaw axes.
But no one pretends they can do it by 'sensing it' other than by seeing it with those Mark 20 eyeballs. And while one can see a slip or skid by reference to the horizon, it can't be done accurately or easily. So the primary instrument used is the yaw string. A piece of yarn taped to the canopy or tied to a pitot tube, centered right in front of the pilots eyes. Just like you 'step on the ball' to get things coordinated, glider pilots either pull the string with the pedal or whack it with the stick.
Unfortunately, a yaw string won't work with a SE tractor but the ball will do.
I think the 'trick' to flying coordinated is to make the ball part of your scan and generally try to get a movie in you head of what a coordinated turn looks like relative to the horizon. But probably most important, just figuring out how much rudder a particular plane needs to enter a turn, maintain a turn, takeoff, climb out, etc. Coordinated pilots anticipate what's needed, apply it, and make the ball part of their scan.
But I'm not a CFI so there may be better approaches.