bldc motor torque controller
Implementing a current loop should not require field oriented control.  You should be able to have a PI controller driven by a current feedback (e.g. see here: http://irtfweb.ifa.hawaii.edu/~tcs3/tcs3/0405_Servo_review/onaka_docs/2000_articles_control.pdf and here: http://www.drivetechinc.com/articles/curbldc3.pdf ).  I would think you need two independent loops/feedback for a three phase system.  What speed are you running your loop at?  What are the stability issues you're seeing?  You should tune your current loop with all the other loops disabled.

Since you mention "average" current and measuring on one phase I'm wondering what exactly you're doing.  Closed loop current control is traditionally controlling the "instantaneous" current and is the highest frequency/bandwidth, innermost, loop in a closed loop motion control system.