>What's a good way to work out this situation? Help!

> Content that, thanks to the abundant Shannox trash, takes an hour longer than it really should.

You take an hour on Shannox trash?

A start with a blast from the past -- Kyth's StratFU guides on chain pulling stuff. It's Naxx stuff, but the general ideas are still valid:
http://www.youtube.com/watch?v=3fxOW3L890c
http://www.youtube.com/watch?v=QbKZd5ShJ7E

Chain pull trash. Have healers pop mana /raid cooldowns (tide, hope, plea, DS, tranq, commie totem.) Lust if you pull to much, brez, etc. Go towards Beth first, kill her, then go to Rhyo. By the time you've cleared shannox trash toward Rhyo, you should be fine. You can skip or quickly kill some of the trash on the way to Bale and Alys/Rhyo.

>Alt/offnight runs don't really help, as we are a small guild on a small server.
> She tried to PuG the content but some tool ninjad the essences, despite her clearly asking if anyone else was on the questline.

If she's pug leading have her go to the armory and check the gear of everyone who's class is capable of being on the quest before inviting. I think you can also check quest logs to see if anyone else is on the same quest as you.

What's going to happen as you progress in DS: You're eventually going to be clearing the place in less time than you scheduled for raid. Take some of the extra time to go back into FL to do a few bosses for the staff -- a lil more gear and a lil more time away from the content might make it less of a bother.

Motivation: DS bosses have tight enrage and DPS requirements. Staff will help you to get things down more quickly to meet them: Ultraxion, Spine, Maddness. If you're clearing these already -- you're likely to be in heroic modes soon anyway and that means more enrage timers.