This business of heading versus track seems to crop up quite regularly and, speaking as a controller, I find it quite worrying. If I give a pilot a heading to fly I mean FLY THAT HEADING. If I want you to take up a track to a particular place, I'll tell you to route direct to X. If I don't much care where you go, I'll clear you to go on on your own navigation.
When I give a heading I've taken into account the wind. If I've got it wrong I'll correct it.
If I've given a heading that isn't working well for the pilot for any reason, tell me about it and between us we'll sort it out in such a way that doesn't cause problems for other pilots.
A pilot who decides that when I said HEADING I really meant TRACK will cause problems for everyone at some point.
Things may change in the future with RNAV and stuff but, for the moment, if the controller says heading then he/she means heading. So please use HDG mode - that's what it's there for!
As to the original question - the same applies. If the closing heading isn't working tell the controller - if it's not a problem to other aircraft and you ask to sort it yourself you'll probably be cleared to do what you want.