Hey mate,
I'm not the best at dissecting logs so I can only point out some of the easier things to see.
1. Don't use trueshot so early - you're wasting focus by popping it before you've used an ability.
2. Potion of deadly grace are really good, using 2x potion will show a huge increase of dps. If they're too expensive maybe try potion of prolonged power.
3. Always start with windburst right before pull (I assume your guild uses pull timers?) and THEN trueshot+cooldowns -> barrage then go onto your rotation.
3. Use windburst and barrage on cool down, fight length/20 seconds = how many casts you should get off of each. I don't know if it's movement or what but that's not happening.
4. Use your 2nd trueshot at ~25% (and 2nd pot - if it's prolonged power make sure to use it earlier to get full minute) because of the artifact trait we get a lot of crit with < 25% hp on the boss.
5. Never stop casting. Move less, you don't need to move much really, don't let it stop you getting globals off. The more casts per fight the more dps naturally. Use things like disengage to your advantage for breath etc and make sure to finish your cast before using it. If you know breath is coming in the next ~5sec you can delay barrage or an LnL proc for that movement.
Good luck mate. Get onto the dummies and practice moving around without hindering dps too much. When it's coming into the phase where she sucks all the shit in, get into a good spot beforehand - maybe when there's some downtime in your rotation. That way when you've got stuff going on you don't have to move. Get into the practice of finishing your cast and then moving, only the amount that you HAVE to. Never move further than necessary.
Good luck mate.