Are you able to share a little bit about what you're trying to achieve, without getting too close to that line your employer has set you?
Heat maps and mouse tracking are interesting, but not necessarily the most reliable way to analyse usability issues. Given you have Balsamiq and Camtasia, I'm guessing you've run some usability tests on interactive prototypes? Running a handful of them should have given you a collection of rich, qualitative data that should help you understand where the big hurdles are, and identify a few patterns to a) help you prioritise what you should focus on, but more importantly b) help you understand why certain features, navigation paths, or ways of doing things are important to your users. This "why" is far more important than any numbers that a simulated heat map might give you (if it's web-based, then it's only simulated—accurate eye-tracking usually requires expensive gear to do properly, and in my opinion is overkill in most cases).
Quantitative data might feel more convincing, because numbers are black and white. But they require additional insights to gain understanding. You can only get that understanding from observing people use your product, and by asking them questions. And you don't need fancy tools to do that.
Hope that helps.