Using MATLAB for an extensive-form game experiment with multiple participants

A colleague and I have programmed an experiment in MATLAB and we're applying for funding to run the experiment in a behavioral economics laboratory with human players. Each experiment session has five participants and each participant's decision affects the options and payoffs for players making subsequent decisions. Currently our plan is to bring the player whose turn it is up to the main computer terminal in the lab to make her decision, then have her return to her seat and call the next player. This way the entire experiment can be run on one computer. The problem with this is each session requires hundred of decisions, so this could take a very long time and require a fair bit of coordination. Ideally we would be able to run the experiment on a central terminal (or online) and beam the GUI to the computer of each player upon her turn, solicit her response, and then have the central terminal use that response to set up the next iteration (and beam a new GUI to whomever is next). Each player will have their own computer--the difficult is in running the experiment across those computers.

I've heard of people running experiments like this with programs like z-Tree, but I fear it would be impossible to reimplement our quite complicated experiment in the z-Tree programming language (which is somewhat limited and a bit clunky). Does anybody have any ideas of a way that we could do this either directly in MATLAB (perhaps through MATLAB online) or using MATLAB in conjunction with other 3rd party software?