Sorry - I don't know IPA. But 'close' as in 'nearby' is a short sound, similar to 'gross', or 'morose' whereas 'close' as in 'shut' is a longer sound, more like 'grows'.
There was a TV programme recently called 'The Closer', about some sort of detective. It was quite funny, as the local announcers got confused and initially introduced it by pronouncing it to suggest 'the person who was nearer', and eventually changed it to sound like 'the person who closes things'.