We have a similar environment as yours. In the past 10 years where a user would submit a software request form, once approved, then we install the software. As you can imagine, it would be nearly impossible to go back 10 years and trace everything to make it compliance.
We used the forget about the past and moving forward approach if you know what I meant. We picked a product to monitor and track (Adobe Acrobat Pro/Std). Then we picked a month, for example April 2014, anything prior to April 2014 would be archived considered "inaccurate data".
There's no wrong or right way to track or monitor a software. You need to pick a product first to setup a process and tweak it as it goes before starting to monitor dozens of software. Hopes this gives you some idea.