I am not a lawyer by any means, and am certainly not qualified to offer "advise" but what I would be doing in this type of situation...
-I like the keep quiet approach. I wouldn't give them any more than is absolutely, legally necessary, for great reasons pointed out already.
-I'd look into some way to record audio calls. I realize the probability is very small that you'll have much phone/audio correspondence with them, but I would want to have that recording if I ever needed it. I can't imagine the "...profit center ... dinner and drinks..." comment would resonate very well, should the case ever come before a judge...
-You mentioned that whatever the issue at hand is, has some potential advantage for their competitors. I would be doing this quietly & discreetly, but I would be looking into which of these competitors of theirs you could collaborate with. If this patent really is bogus and they are planning on pursuing a frivolous suit against you, I would personally not rule out using their competitors as leverage. This could be terrible advise, but I'm beginning to learn more than I ever wanted about sales & business politics, and it's very real.
-These allegations are being run by the company's lawyers & legal department. They have a boss, and they do not represent the intentions of all persons & departments within the company. If there's anyway to take this power away from their legal team, I'd consider that as well... I don't know what that would look like, but you're a creative guy. Maybe consider ANY business ties that you may have to any of their suppliers, or perhaps the negotiated "settlement" of the issues in order to prevent the opening of the issue to all other competitors, including the Chinese if their patent was found invalid, (even though we all understand that this is an almost irrelevant argument, since you publicly disclosed it,) or some other way... Basically any way possible that someone within their company would call off the dogs...
(If they are running a profit center, then this whole case could be a net-negative financially for them, especially if you have any real chance of winning in the end. Some savvy financial guy might not like that, especially if the legal team creates their own initiatives without any kind of guidance on whom to pursue... This might sound incredibly naive, but again, I personally wouldn't rule it out...)
Other good advise from far better qualified people here. Good on you for keeping a healthy perspective, and considering your employee's and their families well-being too. We wish you the best...