Process Standardization Project?

I am working on a project and I'm in the defined phase.  As my project team researches into the process we have found that we have no process map or any standard to do the process.  In fact, we have several different departments/divisions all doing this process differently with no policies or procedures.

Because of this lack of standardization, there is no "X" data to be collected for my "real" problem I am trying to solve.

My question:

Can you run a DMAIC on variation of how we do processes?  Or is it just so obvious that we need to standardize that there is no point in running a DMAIC cycle.

My organization is looking for some quick wins/changes and I thought using the DMAIC on process variation could give me that.  If this is the case, what is the Primary Metric?  Would you run a Gage R&R to determine the reproducibility and repeatability prior to improvement and then run another after?

What are your thoughts?