your stats look good and you're winning at a good rate.
If you could have a positive return from non-showdown pots but be a net loser, that would be bad - right?

There are lots of ways to win poker. The weaker the games you're playing in, the less you should be focusing on non-showdown winnings (fullring, anyway).

However, non-showdown pots. Some questions:
1) are you c-betting too much? in inappropriate situations?
2) are you bet folding too much? especially rivers where check-call and check-fold are often forgotten lines.
3) are you giving up one street too late?
4) are you forgetting to take free cards with draws?
5) is your betsizing too weak?
6) are you identifying the players who don't fold? those that fold easily?