Bluetooth sync with Local contacts - cyanogenmod G'day,

I have a SGS4mini (I9195) with cyanogenmod 11 (4.4 kitkat) and have most of my contacts "local" i.e. not synced with google. I have successfully paired it with my (Citroen) car and can place and receive calls fine.

However, the contacts in the car only show those from google and maybe those from the SIM card - the normal contacts do not appear in car's contact list. It doesn't show a name for a local contact if receiving a call nor in the recent calls list nor can I choose it to make a call.

Could someone suggest how to fix it or how to get more information about it? It seems the problem is not so common, I'm willing to help fixing if it could need some fixing/coding. Thanks!
By chance, I found out that the local contact show up in the car when at the time before I start the car (or activate phone's bluetooth goint to the car?) I go to the Contacts App, select the options (3 dots), select (sorry german version) "Kontakte zum Anzeigen" ("show which contacts") and then, instead of "all", select the "phone only, not synchronized". 

Drive away and have the local contacts visible in the car (though not the google ones then, but most phone numbers are local here)

Additionally I found out that I can "send" the contacts from the phone to the car, but then there are too many in the phone so that the car can't hold all of them, and I'd have to send new contacts by hand...