I'm not a lawyer, but a number have commented on how this would likely go.
The general provision regardind discovery for Washington are here. In summary:
There are certainly grounds by under which you can refuse to hand over materials (ie they're not pertinent etc) and try to get a speedier trial. But in order to make that case, you need a decent lawyer, which is expensive. And all that does is get you past the discovery phase. Without a decent lawyer, you're just going to lose the trial itself.
Yes, you probably need a lawyer just to explain, in appropriate legalese, that you are not defending any copyright claim, that you certainly did copy, as permitted under the OGL, and that your defense is that you have a licence under the OGL. That does not seem like a difficult thing for a lawyer to do, though.
If you are not disputing any claims for which Discovery is relevant, the two sides are agreed on the facts. I cannot see any basis for forcing Discovery.
(BTW this does again raise the point how much more vulnerable companies are when they rely on Copyright rather than Contract. It's easy to see how Discovery is relevant when a company tries to make a D&D-like RPG without infringing copyright in D&D.)