I think your assessment is correct: we have lots of people here to answer, but we aren't seeing many new questions. Inertia is keeping the new questions mostly on SE. I, too, have been going through the lottery tab, casting votes and looking for things I can add useful answers to, but we need new questions too.
I haven't spent time on SE lately but I still get the Writing.SE newsletter, so I see the titles and opening words of some new questions. A lot of them do not seem to be high quality, but some are promising. If you see a question there -- or anywhere else (mailing list, Quora, Reddit, wherever) that's a good on-topic question, please feel free to bring it here! This was something Joel and Jeff actually advocated in the early days of SO -- they'd see a question somewhere, ask it on SO, get an answer, and report back in the original setting. So long as we cite appropriately, we can do that too.
Doing that will provide some questions, but it won't provide a lot. That leaves two other paths: (a) ask more questions ourselves, and (b) attract more people to this community. Secespitus suggests in a comment that we consider contests again, which would address (a). What other thoughts do people have? (Anybody who wants to pitch a contest, feel free! What organizing theme might we use? Last time it was tags; we could do that again or do something else.)