From the OP 'Our userbase is constantly expanding' so product is obviously not dying. Then he says "these users expect modern conveniences like intuitive UI and documented processes". Well do they? Or does the software do exactly what these new customers want it to do? This sounds an awful lot like "I don't like the UI and I want to change it".
Documented processes is one thing. Get your documentation up to scratch.
But sure as fuck don't mess with a long term UI because you think it should look modern. In business the first thing is does it work and does it work well. The next thing is why am I wasting time learning a new way to do an old trick?
There is a reason I run linux mint and not Ubuntu or Windows 8 / 10. They fucked up the UI.