We already have legal advice. While advice from random strangers ought to be take with a pack of salt, random strangers have little vested interest in the topic and nothing to lose plus a very fresh perspective. Hence there's a likelihood of unbiased (if a tad uninformed) opinions.
So the things you say, and danieltillet says, are basically the things I'm looking for. And I hope more folks chime in too, particularly if they've experienced situations like this.
We are indeed starting to double/treble down on sales (thanks for the little "slogans" too). The majority opinion leans towards a fight, since for each seller we have BigCo has 100-1000. Their scale can let them get away with a cheap knockoff that mostly replicates the functionality but lacks in UI/UX. And I'm sure you know sellers are more interested in the scale, margins, etc. of a platform. So while we can take the market, it might have to be off more than just 1-2 patents.
Besides, there's always the hope that a court side with David rather than Goliath. And if they don't, and we lose the appeals too, we end up where we started and can only outsell them. And if we can survive long enough to win, we might as well get paid for lost revenues.