Having not seen the resulting MKV, and basing all of this just on your HandBrake settings:

I'd go with a higher bitrate, or consider using the "Constant Quality" setting at around RF=20 or 18. (Note that using the CQ setting negates the need for two video passes.)

I'd also not make it anamorphic, as I know that can cause compatibility issues on some players. But this may not be a problem. (I, personally, always encode anamorphic, but that's mainly because I know that what I'll be watching them on can display it properly.)

Otherwise, it all looks right to me.