You say your company wants to spend less and achieve more. If that's true, then there's really no better value than Esri software. Esri is the gold standard with GIS. Nothing else on the market is really at the same level in terms of accuracy, scale and capabilities. Open-Source GIS is getting better, but it's still very much a work in progress and you need to have pretty good development resources to make those solutions work the way you want them to.
You mention that you have an ArcGIS for Desktop Basic License and that you would definitely need an Advanced License. That's probably not actually right. When you purchase the Esri Business Analyst Desktop extension, regardless of the license level of your core ArcGIS for Desktop software, you receive access to all of the tools in the Esri Business Analyst Desktop product suite and their core product dependencies for the license level of Esri Business Analyst Desktop which you install, which could be either Basic or Standard. That means Esri Business Analyst will not only provide the additional Business Analyst functionality, but will also unlock some functionality that would normally be provisioned only at a higher license level of ArcGIS for Desktop.
The Basic license of Esri Business Analyst Desktop includes the vast majority of the data and tools provided by the Esri Business Analyst Desktop extension. I believe the Tapestry data or some of the Market Potential Data as well as a couple of niche functions are licensed only at the Standard license level however, the Original Huff Model, Advanced Huff Model and all of the real value-add tools and data are licensed at the Basic level.
If your company wants to spend less and achieve more, Esri Business Analyst is really the way I would go. It's not cheap and I recognize that, but in the long run it will probably be cheaper than any other solution you might consider because what you will otherwise be forced to expend time and money to gather data and rebuild functionality that Esri's Business Analyst solution would have provided out of the box, and you probably won't be able to do it quite as well as them.
Here's some links to the Esri Business Analyst product:
Esri Business Analyst Desktop
Esri Business Analyst Original Huff Model
Esri Business Analyst Advanced Huff Model