I can really identify with this. A poor UI will drive user's thought processes. Kind of like the Sapir-Whorf hypothesis (http://en.wikipedia.org/wiki/Linguistic_relativity). When new users come into the organization, their thoughts are shaped by the program used to do the job.
Unfortunately at this stage no one seems to really know the business processes, and the software now dictates the process (even when incorrect). It's quite a struggle.
I certainly bet it's a large struggle. The costs to redesign (based on the real business process), implement, and train users on the new system would be incredibly large. This is another reason to get things correct in the requirements analysis when designing the original software. Unfortunately a lot of software out there either didn't have that process or didn't do it well - much of our software is based on the process that was optimized for a paper-based system.
Does anyone have any experience with optimizing processes like this or data about those costs?
Unfortunately at this stage no one seems to really know the business processes, and the software now dictates the process (even when incorrect). It's quite a struggle.