Harper should always bat in the 1st inning.

Batting third, if batters 1 and 2 make outs, the only damage Harper can do is hit a homerun. If he instead is fourth, he could hit that same homerun leading off the second inning. Not much difference. If either batter 1 or 2 gets on, then Harper batting fourth will bat (assuming no DP).

If batting third, with two outs nobody on, he hits a double: wouldn't you rather have that same double with nobody out?

And, batting fourth, there is more chance that he will come up with two or even three runners on, than batting third.

I think your most productive hitter should be fourth.