Host travis on your own

The matrix expansion component is not open-source if @BanzaiMan is to be believed, and I couldn’t find the build scripts for the images in use.

Travis offers on-premise installations which is exactly what you are describing.
The deal is that it’s going to be cheaper to pay them for installation and support than try to do it yourself (yes, your workers could be dirt cheap if you are using slave labor or something but in this case, they’ll probably be unable to set it up within a reasonable time and keep it running smoothly).