I'm trying to create a Korean font texture, but the characters all come out rotated 90 degrees counter-clockwise. Anywhere else, like in Word or Firefox, the characters are not rotated.

You've chosen a font that starts with @ in the name. This is a special version of the true type font where the asian characters are rotated by 90 degrees, to allow writing top-down texts in normal word processors. You should choose the font without the prepended @.

This is also documented in the known issues of BMFont.

Regards,
Andreas