It's simple what I'm trying to do, grab. That is my goal in every match, all my movements are to either space or bait a certain move to punish them. I'm neither approaching or camping, just waiting. I'll only desync if I'm sure it's a safe opportunity, since both IB and Blizzard (the main tools used in desyncs) are both quite punishable on start-up and end lag.
If I'm synced and just running away, it is either because I have the lead, and they're going to have to approach eventually, so I wait. Or it's because I'm thinking about what just happened, usually because my last approach got me punished. I create space to think instead of continuously approaching when I'm either behind or I just had the wrong read on the opponent. I pretty much only play with reads and punishing.
If I'm separated from Nana and you see me moving away, it's because you have more control over a separated Nana when further away (her SDI is better, and it's easier to tell her to jump, sometimes b-reverse an ice block). I only move in closer to a separated Nana when the opponent can be punished for attacking her (many don't allow you to), when the opponent is no longer between myself and Nana so I can get synced, and when I see an opportunity to tell her to air dodge, tech, get-up attack (all accompished by hold shield near her) or simply attack with n-air or a smash if she is grounded.
And my approach option isn't just sliding shield grab lol (although even if you don't think it will work, it's worth doing since it's hard for most characters to grab you, and is one of the most threatening tools ic's have, leading to some type of reaction or giving your opponent less time to think when you believe they are starting to figure out how to get past a wall etc.).
I also use sliding spot dodge extensively, since it avoids shield push from attacks, crosses up, and avoids grabs. It's a high-risk high-reward tool to use since it can definitely get you punished, but if you predicted correctly, you get a grab and a stock.
Otherwise, why approach, why desynch? Just camp in their face, spacing yourself and the occasional aerial. Approach just close enough so that you are at your characters optimal range, but not commiting to anything. Something you see from many characters like MK, Marth, Luigi, Kirby, and much of the cast. Get close enough to close the gap and punish any bad decisions as you wait for them. It's a style I see many top players use and have adapted myself. IC's frame data just isn't good enough to guess wrong and commit without getting punished (unlike MK, Snake, Diddy, and other top/high tier characters)
So I hope that helps you to see what I'm thinking and how I approach the game. Thanks for the Pit match-up advice though... since I have no clue what to do (or ever had to have a clue >.<). Will definitely keep that in mind =)