Hello there!
I can't speak for MeshCam and Cut3D - they are certainly both well regarded. I would recommend you try the demo versions of each (before coming back to CamBam

).
I would say that the latest 3D machining operations in CamBam are very new and thus not as well tested and refined as the 2.5D operations, which are CamBam's biggest strength. However new CamBam releases appear regularly and improving 3D performance is certainly high on the development list.
I have been contemplating trying some 'manual' 4th axis objects myself.
It is certainly possible. The current 3D routines support a front face and a back face option. To do other directions, you would need to copy the mesh and apply a rotation transformation.
My idea was to machine a pair of hexagon plates, with registration marks (pin holes) on each edge. The stock would be mounted between these plates, then machined and the plates rotated between each 'face'.
Then I figured it may be time better spent setting up a proper 4th (rotary) axis on the machine. The same toolpath tactic could be used, and gcode added to each machining operation footer to rotate the axis for the next 'face'.
Although not a high priority, I would like to add proper 4th axis toolpath support to CamBam at some point so this method would perhaps be a bit of encouragement to get that underway.