I also use SolidWorks and VisualMill.
Most 4 axis work can be broke down. Typically - 90% of mechanical operations can be done with 2.5D Cam with an indexed move to the next face and more 2.5D machining.
The same can be done for more complex geometry that requires 3D programing.
Even stuff that you swear must be done in full 4 axis can usually be broke down into 3 + 1 toolpaths. It takes a lot more programming time and effort but is do-able.
What I am getting at is that you can likely get done what you are trying to do with free software, a bit of hand coding and using your noodle (aka brain) creatively.
I don't think you will find any Cam that will do 4 axis continuous toolpaths for less than $3g
www.integratedmechanical.ca