Well, you could theoretically combine the S-Log2 linearization function w/ the S-Gamut3.cine to AP0 matrix, thus creating a hybrid transform from the two existing CTLs. However, as you yourself note, this is not manufacturer recommended and as such will not be available as a built in transform in any color correction tools (e.g. Resolve, Filmlight, etc). However, support for S-Log2 or S-Log3/S-Gamut3Cine are built in. So I would really question why you feel you must use S-Log2 with S-Gamut3cine?
The differences are in the white balance scale factors and the illuminant used to optimize the color conversion matrix. I would recommend choosing the option that is closest to your capture environment. If daylight is closest, go with that.
10-bit and 12-bit integer. Most implementations beyond the camera are floating point so you shouldn’t really even see this choice in color correctors, etc.