Hmm. Generally, here, I get the impression that, while black can hold the blockade on d6, this does cause passivity in his position. I never feel like white has a similar obligation -- he can sort of do what he wants, but black often wants to keep something on d6 and he doesn't get any special play on the kingside or queenside in return for this.
It looks like white has a safe advantage but at the same time black is very solid. I would prefer to not have to blockade d6, but, it's perhaps a manageable problem for black. My guess as to why you may have had trouble playing for a win here is that the position is fairly static -- the pawn structure is likely to remain similar for a long time.
Compared to, say, a king's indian where white is often pushing c4-c5, this blasts open the position a lot more dramatically. Here on the other hand, it's hard to open much activity in an effective way. So you exchange winning chances for safety. White has a safe edge, but it may be just a tad on the drawish side. On the other hand maybe you just had bad luck.
In a tournament last weekend I got a position with a protected passed d-pawn vs a queenside majority, and screwed it up rather badly, allowing an 1850 (a couple hundred points below me) to draw me. I got the same pawn structure during an online blitz game a couple days ago, and won, but felt relatively planless again. I'll post both games below.
My understanding is that the d-pawn is a long term asset, but if black just blockades on d6, it's hard for white to find play, and black still has a mobile pawn majority unlike white. I found it difficult to determine a course of action in both games, and probably wasted a lot of moves. Here are the games: