Some Google-Fu led me to the book Caverns of Socrates by Dennis L. McKiernan, published in 1995.
The description on the book link matches a lot of what you give, though you remembered four of the five characters. Areas that match have emphasis added:
They called themselves the Black Foxes, a group of adventure gamers who had proved the big winners in the virtual reality tournaments. In the "real world, " they were Alice, Caine, Eric, Meredith, and Hiroko - respectively, scientist, doctor, writer, antiquarian book expert, and art gallery owner. But when they became the Black Foxes they were transformed into: a pathfinder, a master healer, a warrior extraordinaire and leader of the Foxes, a bard whose music worked surprising magic, and a syldari Shadowmaster, able to bend the darkness itself to her needs. They had been chosen to participate in a unique experiment to help test AIVR, a supercomputer with artificial intelligence. Avery, as it was called, would create a virtual reality universe so convincing that the Black Foxes would forget the outside world as they undertook their journey. And so, under the watchful eyes of researchers, the contest between humans and machine began. Yet no one anticipated losing control of Avery. With the minds and souls of the Black Foxes trapped inside the machine's own private universe, their only hope of returning to the real world lay in carrying out a dangerous and deadly quest to defeat the DemonQueen and beat Avery at his own game....
I've never read it, but it seems to match.