I think that theory has the inside track....
My LA team is starting yet another season by dropping faster than a lead weight, despite having as good a collection of starters I'm likely to get. When your team constantly sucks you do get nice draft choices, and they're finally in the majors.
So I concluded I suck at HBD, but the converse question is, if I didn't suck how would I have built my offense to exploit Dodger Stadium.
Apparently I'm still too dazzled by real-life Dodger teams that had four 30-HR hitters. I've been trying to assemble teams that hit for power and average, with high defensive skills. And the real comic part has been that when I import one of these players via a costly trade, they promptly quit hitting. (They don't always start again after I unload them, right Green?)
When I looked at the first couple of successful teams named in this thread, they were notable for having a lot of position players with very high OBP. There was some power, but that wasn't the emphasis. There's more I can do to upgrade to those kinds of players, so it's something to try.
In all honesty the answer is likely to be that I suck at HBD. Thanks for the help anyway!