Help with DPS in Turn 7 as a BLM

[Malevicton]

In turn 7, how can I keep my DPS high? I'm worried about positioning so much that I don't cast spells constantly. If I'm targeted by Voice, I turn around and don't cast, which wastes 7 seconds. Positioning for shriek (when not targeted), I don't cast at all until the action is finished and I re-position.

This is probably most of your problem, but it's still a good call if you think you might mess up the mechanics. There aren't any particularly rough dps checks in t7, but stoning the mt because you really wanted that last fire cast will be a wipe fersure. That being said, standing around doing nothing kills blm dps. Not as bad for someone like smn since most of their damage goes with dots, but almost all of our dps is from active casts. You should still prioritize not stoning your raid, but as you get the feel for the boss rotation you should start trying to get as much casting uptime as you can. T7 is a practice intensive fight - aka you'll get way better at it the more you do it.

t7 is arguably the most mechanics driven of the scob encounters. As long as you're clearing it, I'd focus your optimization efforts on t8.

Some tips to consider:
Try your best to line up UI for when you're turned around. Doesn't always work out that way, but helps a lot when it does.
You can manaward fireballs.
You can manawall the attacks from the 4 archer adds (doesn't help much but there isn't anything important to manawall).
Depending on how/where your group tanks the first add, you might be able to flare-convert that punk. Helps your dps, but more importantly is just fun to do.

Hope some of this is helpful. The biggest thing I see from what you've told us is to try and increase your time spent casting. There's not wholly a lot of required movement for a ranged in t7, so find a good spot that's far enough to not fireball melee, but close enough that you don't have to move to much for shriek. Then just go turret mode and you'll start wrecking stuff.

Good luck!

Edit:
Aetherial Manipulation is super freaking awesome... but unfortunately it's not great on t7 (mostly cause of fireballs). But on t6, t8 and t9, just think of any time that you need to be somewhere that you are not; this is a good time for AM. ex: in my static, I'm supposed to activate the mine tower that spawns with the second set of towers. So what I do:
1) be killing the dread that will be up before this.
2)wait for a proc during dread, use it to move into the edge of the tower without interrupting my cast (the edge of the tower won't activate it, so don't worry about prematurely setting it off).
3)after the tower's proced, use AM ogcd to get back to the group.
^By doing this I've run to a tower and back without ever losing even a fraction of cast time. Any remotely similar situation is a good time for AM.

Edit-edit:
On races - the stats are negligible, but if you care about the stats anyways, then the best non-lala is the elezen duskwight. They've got the highest base INT.