How good are current AI researchers at simulating complex, first-person emotional states?
Great Question!  One area to look into is Cognitive Architectures.  These are computer programs that solve AI problems by modeling how humans think and feel (emotion).  Here is a brief overview.

Prior to the mid-1980s the study of AI was concerned with creating general intelligent systems modeled after flexible human thinking (Fahlman, 2012).  Researchers in AI used findings in cognitive psychology to guide their work.  

Currently, there has been a shift away from this approach.  The current trend in AI research is towards solving problems with “knowledge-lean” statistical methods which are data intensive and learn less efficiently than humans.  (Langley, 2012).  Thus, the AI field has shifted away from human-like models and toward "ideal" models.  

However, a few AI researches still focus on creating intelligent systems modeled after the way humans think.  These researches work with Cognitive Architectures--Computer programs modeled after humans. The Office of Navel Research's Human Computer Interaction lab is actively working to create intelligent agents that can interact with humans.  

I believe that the study of Cognitive Architectures is an interesting area of research for investigating how to create human-like systems. 

Fahlman, S. E. (2012). Beyone Idiot-Savant AI. Advances in Cognitive Systems 1, 15-21.

Langley, P. (2012). Intelligent behavior in humans and machines. Advances in Cognitive Systems 2, 3-12.

Taatgen, N. A. (1999). Learning without limits. From Problem Solving towards a Unified Theory of Learning(dissertation). Groningen: Rijksuniversiteit Groningen.

http://www.onr.navy.mil/en/Science-Technology/Departments/Code-34/All-Programs/human-bioengineered-systems-341/Human-Robot-Interaction.aspx