Update: Last week I called to cancel my HA Mastercard. It was pretty easy and painless through their automated system. Here's the kicker: the automated system indicated that I was eligible for a refund of my $99 annual fee. The same annual fee that Barclays denied upon appeal.

I called them today and requested a check for the negative balance, and it should arrive in 7-10 days. Barclays is honestly a mess, this will most likely be the last card I get through them. Sticking to Chase, Citi, AMEX branded cards.