Those bars look like they have a really big "drop" to them. Am I imagining that?

In looks likes the levers have been mounted pretty far down the bars as well. I know for a fact I would bring the levers up -if it was my ride.

Since this is such a big bike - there's no doubt that your back is suffering. Its the physics of the situation - a larger skeletal system will produce far greater stress to individual vertebrae when in stressed positions.

It's unlikely that any amount of "core work" will overcome this particular bike fit.

I've decided that you need to get a stem with substantial rise, move your levers back.

This is a severe change - I recommend. And if you keep the existing bars, your ending fit should be set so that the "drops" of the handle bars lay approximately one to two inches below the top tube. Currently they appear to at least four inches low. (if not more)

I repeat - this is only necessary because of your over all height and size.