I would argue that social skills are more important than a double major. Consider doing a year abroad? Good luck, some of the people you meet will become lifelong friends.
I had thought of going to Singapore as a really cool place to study abroad. Any other suggestions?
If your already willing to pay $50k annually (and I complain about my $30k student debt), why don't you just go to college in Europe, Singapore, Australia or Canada? A Math PhD at Stanford that I talked to said that his University of Toronto engineering undergrad was pretty similar to the Stanford undergrad. It would probably be cheaper, and nicer.
Also, all of those people talking to you about social skills and college, ignore them. Spending three or four years getting older, making mistakes and doing stuff will make your social skills better. Deliberately making your social skills better works much, much faster and can be done anytime, though I must admit college is an easy time to do it.