Treemap, Gantt, Scatter Combination Chart

Hi All! 

First time poster here; I've been asked to create a visual to help Project Scheduling & identify periods of Risk. 

Specifically, the task is to have a single visual which anyone can quickly identify overlapping projects (Gantt), while reconizing their scale based on values such as Fee (Treemap?) and some other features such as color to distinguish project type. 

I've included an image below of what I imagine this would look like:

I have tried different Gantt Charts, but they lack the ability to scale in the y direction. So my question is; is somehting like this even possible or any ideas how I could achieve it? 

Thanks!