FYI for the Boston Red Sox last year (I just chose a random team), the #1 spot had only 133 more at-bats than the #9 spot in the lineup, total, for the whole year. Too lazy to do math but I'm guessing that's like .8 more at-bats a game
So statistically your strategy is hardly detrimental. It actually makes a lot of sense, especially if you have a weaker lineup.
Anyway, as for my lineup.
Well I like to always take one of my fastest player and put him in the #8 spot (in the NL), that way I'm punishing the opposition for pitching around him to get to the pitcher
And I care more about alternating Lefties and Righties, than I do traditional lineup rankings... so for example I will take the #4 hitter and bat him 5th or 6th so that I never have two guys batting consecutively from the same side of the plate. I think this gives me a big advantage late in games, when the opposing team starts going to the bullpen.
So for example, taking the OP's starting 9:
Austin Jackson
Bryce Harper
Carlos Gonzales
Ortiz (DH)
Hanley Ramirez
Brett Lawrie
Eric Hosmer
Jesus Montero
Manny Machado.
I'd have my order as follows:
Austin Jackson
Brett Lawrie
Carlos Gonzales
Hanley Ramirez
David Ortiz
Jesus Montero
Bryce Harper
Manny Machado
Eric Hosmer