CoG I don't do it as a commute but I've done the trip a few times as I live in Killie and visit friends in West End of Glasgow. I also use the moors as a good weekend route.
From Kilmarnock Railway Station you can get to the Western Road which has a cycle lane all the way out of Killie on the Glasgow Road. Go through Fenwick village and then under M77 to join old A77 road which has a super cycle lane made up on inside lane of old road but kerbed off from road. I'd not be worried about the trip over the moors (only about 8 miles from Fenwick to Mewton Mearns and there is always a few cars on the road).
At Newton Mearns there is a cycle lane all way to Eastwood Toll. Cycle route wants you to head off left to Thrornliebank but you can to straight on to where Tinto Firs Hotel used to be, turn left to round toll and either through Pollok Park or straight on towards St Andrews Drive, Nithsdale Road and Gower Street, over M8 and onto cycle route near Castle Grayskull which takes you over the Clyde.
Might be worthwhile doing it one way for a while to try it out. Coming back is gently up hill all way out of Glasgow until about Floak so a bit sore on the legs as it is also usyually into the wind.
You can PM me if you want more details