Hi Dr. Peter,
Just thought I would share the initial results of your suggestion because they appear to be so dramatic!
I put it a rel=alternate tag on every page indicating the .edu.sg version of the URL for "en-sg" and the com version of the url for "en".
From MozAnalytics: Before
Rank 1-3: 4 keywords
Rank 4-10: 21 keywords
Rank 11-20: 3 keywords
Rank 21-50: 2 keywords
Rank 51+: 216 keywords
From MozAnalytics: After
Rank 1-3: 50 keywords!!!
Rank 4-10: 19 keywords
Rank 11-20: 3 keywords
Rank 21-50: 13 keywords
Rank 51+: 167 keywords
That's pretty crazy in under a week - Not sure if its 'real' since I never personally went to check rankings on these keywords, but wow! If the MozAnalytics information is correct I am blown away! Unfortunately its for a niche site in a tiny market so its not going to lead to fame and riches, but its still an amazing result!
Thanks so much for the great advice
Alex