“This leaves us with an integration paradox: why does the information content of our conscious experience appear to be vastly larger than 37 bits?”

My suggestion to this paradox is that our consciousness is linked to every conversation that ever happened in the past and every conversation that will happen in the future.
Maybe our consciousness is stored, but not in all of us or our brains but in our conversation.

I figure we have about 1,635 trillion conversations to go before we reach the singularity. That is if it was to occur at the predicted year around 2044.
Based upon 8 billion people conversing 20 times a day, every day for the next 10,220 days, we have 1,635,200,000,000,000 conversations till then.

But then if we factored in to how we could improve our conversations then maybe we could speed up our consciousness process. And maybe us reaching this Singularity is based upon us achieving a certain level of consciousness.

ie I have a theory that conversation, ideally, is for converging and diverging that forms a constant double helix shape, that has an ideal prescribed wavelength and amplitude.

https://en.wikipedia.org/wiki/File:Counterbalance1.gif

But at the same time as there are many types of consciousness there are many types of conversation shapes, all at different levels of efficiency. 
I think that if we learned to embrace and respect the diverging stage of conversation would help our consciousness improve greatly (and reduce conflict and war)