I note the common thread - the SkyView EFIS and autopilot is ?on rails? when following a GPS LP approach, but not when on a non-gps approach.
The SkyView coupled approach is only as good as the input is it getting - from a GTN-650, 430 or whatever.
I started flying with a dual SkyView and GTN-650 install in 2012. The SkyView autopilot was dirt simple to configure and would hold the plane on course and altitude with amazing precision. Even dialing in a new altitude it would follow the chosen VS better than I could. On a GPS LP approach it would hold the GS & CDI needles dead center. I too however noticed it was not as accurate on non-GPS approaches. As I demonstrated the autopilot working properly I attributed this to the inherent difference with the non-GPS approach and the GTN-650.
I suspect I could have gone into the GTN-650 to tweak non-GPS error rates, but it worked well enough for me and I did not want to screw up the GPS functionality.
My recommendation - do what I did and first verify the autopilot does what it should, then go look at whatever you are using to feed the ARINC module.