Pay the extra few $ per gallon and get a pva with extended open time. Adhesives are not a place to be "cheap" and handyman tricks have no place in professional work.
I would not take any chances. Diluting the glue with water may not even have the desired effect. It could even speed up the dry time. You would certainly change the viscosity.
Diluting PVA as glue size certainly works, however we do not use glue size to "glue parts together" so this does not provide a reliable indication on affects this dilution may have on adhesion.
If you add water you are effectively changing the formulation of the adhesive. Without a background as chemical engineer with experience developing adhesives, and knowledge
of the formulation at hand I highly doubt you would be qualified to understand what implications a change could potentially have to adhesion, or the working properties of the glue.
As a professional woodworker you should 1. choose an adhesive that has the desired working properties, and open time. 2 use this product within recommended application following the manufactures prescribed guidelines for use.