As someone who is also a bit on the tall side (between 6'4 and 6'5"), I've lh, lb, and lhlb bats. I've found that all three work for me, but that the key thing is the middle position.
Where is used a lower middle before, the middle set more mid on all works well. Interns of balance, it very much depends on the bat. I've a beautifully balanced b3 lh that picks up weigh better than my similar middle lb, but is equivalent to my lhlb.
If you are after something bigger than sh, I'd really recommend visiting a maker and having them make and balance it for you there and then as it really makes a huge difference. Good luck!
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