For the particular document you sent, there is only one reaction used in the reactor. This is the one with the equilibrium constant in the order of 1e12. If this is what you want to solve I suggest you use a fixed conversion reactor and let all oxygen convert.
If you want to mix this with another (the other) reaction, this will not really be feasible with the type of solver that is used. It wants to solve for a reaction extent such that the ratios of concentrations are so that the specified equilibrium constant is met. This requires a near machine precision solution (if not beyond machine precision) of the reaction extent. It is possible to solve such systems, but not with the formulation used by this reactor.
Solving for the particular case of your two reactions is rather straight forward (presuming you are not interested in how much oxygen remains exactly as it is near zero). You are looking for one degree of freedom, the extent of the reaction that is not taking place to full extent, such that its equilibrium constant is obtained; during the function evaluation you perform the other reaction to its maximum extent. Simple to do in for example a Matlab or Scilab unit operation.
In this particular case however the overlap in reactants appears to me such that there is an even simpler solution: first react all oxygen away in a fixed conversion reactor, then perform your equilibrium in a second reactor. I sent this setup back to you via e-mail.
I have put support for irreversible instantaneous reactions on the list of things to do.