In all my time commuting in/out Glasgow Central and Paisley Gilmour Street, can't say I've ever seen a 314 heading to/from Ayrshire - which is not to say they've never been (there's evidence above) but obviously a pretty rare occurrence. There was the regular 2 x 303 diagram between Central and Ardrossan - something like 1715 ex Central? So I guess 314s might have worked that during the transition from 303s?
As others have said, a pretty sizable proportion of the Inverclydes are currently 314s.
I haven't checked the Inverclyde WTT for a while, but at one time all the paths were for 75mph units regardless of actual diagrams. I'm not sure there's actually that much (if any) of the Inverclyde line which has speed limits above 75mph?