I think you are actually more well-equipped than you might think! For my part, I am graduating with a BA in humanities and liberal arts (history and philosophy) with no research experience. I will be attending a research masters in experimental psychology next year at top-5 world school. So as you see, it is definitely not impossible!
Peaceful Learner gave you some really good tips and I mostly agree with them as well. UChicago's program sounds very similar to your research interests that you mentioned. One thing that wasn't yet mentioned though is that if you want to apply to purely psychology/sociology departments (i.e. no behavior/social cognition ones), then it will be harder for you to make a case for how your previous education connects to and enriches your current research goals. Although it may be harder, it may prove to be a great advantage for you if you can clearly connect your interests from your MBA to your current interests. Research in psychology is already quite interdisciplinary and covers a vast area of topics in both quantitative and qualitative research, so your knowledge of and training in some more specific area (such as business and customer related behavior) may be very beneficial to your application. It may even become a deciding factor for some programs where you need to distinguish yourself more from the general applicant pool with background in psychology.
As I said earlier, you (as well as all the other people, who replied to your questions) do actually have backgrounds in some very related disciplines to psychology and sociology. Nowadays even computer science, theoretical physics, or engineering are quite related to some topics within the field of psychology.