Install the old LFR loot system again. I just did all 16 on my 2 alts and got one item on my Druid: The chestpiece I was already wearing.
The old system had its downsides, but the one thing it did better than the current system is rewarding participation by giving players a chance to roll on an item. It's extremely unlikely in the old system that, on 32 bosses (equaling 4 Dragon Soul LFR clears), I would have seen only 1 item pop up that I would be eligible for.
It's the items drop that gives us a surge of hope to requeue every week. The satchels of gold do nothing of that, they are demotivating. Losing a roll is only part of the raiding experience, and doing all of this (the item drop, the roll) in the background is futile. There's a reason people love to gamble: It's all about the thrill of getting something, maybe winning maybe losing, not about the reward itself. The current LFR system is the latter: They only show you what you won.
They were already looking into that. Going back to the old system is just not happening. It was awefull.