This "answer" records what I did this year and how it worked out. I drew from several suggestions in other answers here.
Some context: the two seders had different but overlapping groups of attendees. One has always been a "when do we eat?" seder; the other spends more time but replaces a lot of the traditional content with other readings and songs (mostly Zionist). It was hard to get the leaaders of the former to pause for any discussion, though we had some brief conversations farther down the table and a little during the meal. The other one ended up having better prospects.
Eytan Yammer suggested: Go around the table and have everyone finish a sentence "slavery is..." "freedom is..."
This idea really appeals to me. It makes it personal. I recast this as: Pesach is about freedom. We can be free from things and we can be free to do things. How are we free this year?"
What I learned: I think this would work well for a seder with friends, but the idea fell flat with a group of relatives who are there because you're expected to be there. This idea felt awkward to the people I proposed it to before the seder and I did not pursue it further. I will use this idea in other seder settings in the future.
Jake suggested: Get into "round-table" discussions related to the Exodus somehow, in which everyone is encouraged to voice their opinions on the subject at hand.
This worked, albeit not in the way I anticipated. I went prepared with ideas to throw out for discussion and people didn't much take the bait -- but it led to them asking questions, and once it wasn't coming from the most religious person at the table it worked well. The conversations were not necessarily deep, but people asked questions and offered answers -- score. (During the hurried seder when I saw somebody trying to speak I directly encouraged that person to ask his question -- if not then, then the following night. This happened.)
Seth J suggested (in a comment): have everyone go around the room reading and following the Haggadah for as long as everyone seems willing/able to pay attention.
This practice naturally arose at one seder (the latter one) and had to be pushed a little harder with the other. Sharing the reading increased participation (and that's a keeper); some people, however, read as quickly as they could to get it over with. Perhaps an explicit invitation to pass if you must (but we'd really like you to read) would address this.
Seth also suggested good wine: check. :-)
Eytan said: when you prepare think of questions more than answers.
Yes. Questions invited discussion, and a lot of them came back to people looking to me for answers but that has a very different dynamic than offering a d'var up front. (And none of my answers were long.)
Jake suggested more singing. One of the two seders is usually fairly musical and the other not; I was able to help both of them do more music by the simple expedient of just started to sing (rather than waiting for consensus to arise). It probably helps that I have a pretty good voice (at least according to the other attendees).
I did not get to try Eytan's suggestions about art or personalized readings, nor Jake's and Gershon's suggestions about table toys/puzzles.
Anything I could do to prompt other people to ask questions -- planting ideas, reaching out to hesitant people, helping side/dinner conversations happen -- worked well. Asking questions about the text, the haggadah, etc worked; asking people to personalize it did not work in this setting (but would in others).
Coming prepared to present material was not needed, or helpful. People didn't want unsolicited teaching, but answers to their questions are completely different.
Sharing the reading among willing participants worked; pushing people who don't want to read to read led to rushed, mumbled reading, not engagement.
Singing worked well, and it was ok to just jump in and not wait for permission.
In the future I hope to build on this foundation.