I finally heard back from Bolivian Mountains guide company! They are one of the few we were able to track down online. I suppose, we could wait to do all the research when we are in Bolivia, but I think we prefer to figure out some of the more complex ideas beforehand.
The idea is a 13-day trek across the Cordillera Real, including some high passes and plenty of amazing views. Followed by heading onto Lake Titicaca.
We'll wait and see what they come back to us with.