I managed to silently replace subsystem by subsystem at a time, and one and a half years later the whole system has been straighten out.
My experience with the Big Ball of Mud has been similar to this. Working in the Financial Services Industry, I have encountered numerous Excel / VBA Spreadsheets and Bloomberg VBA / API code that has been put together hap hazardly by analysts and traders in
an effort to achieve a near term goal.
I dealt with this by introducing small changes in small modules / classes one by one.
Here is an example.
Some of the trading analytics was in spreadsheets (.xls ) saved on network folders. These spreadsheets had hard-wired links to other .xls spreadsheets. Besides that, there was no control over the changes made to these spreadsheets.
When I had to make a few code changes to these analytics and deploy them properly,
the first thing I did was to convert all the spreadsheets to templates (.xlt).
the second thing I did was to create an add-in with menu, that would internally instantiate the templates, so that users don't have direct access to the templates and hence don't make unauthorised changes and bring the setup down.
the third thing I did was to store configuration information for location of the templates in an xml file, and added functionality within the add-in to browse and set the location for this xml file. I used MSXML to parse the xml file and load it
into a hash table style "Scripting.Dictionary" object in memory.
finally, I wrote a .vbs script for deployment of the new analytics, which would take an environment as parameter (ex DEV or QA or PROD) and according set the xml file within the add-in before copying it over to the user's local add-ins folder.
Ofcouse, this is a very simplistic example. But I have taken this approach and used it in more complex application and have achieved similar results. Also, the move from
mud to magic takes quite a bit of time and includes some resistance from some of the end users as they want their "fixes" immediately, so don't expect 'Instant Gratification' in your efforts to change this