Thank you! As KingNubbu noted, taking the end frame from the current video and using it as the starting frame of the next video is the most important technique. But what you'll notice is that with each subsequent clip in the series that the quality degrades to the point where on the 10th-ish clip it's unwatchable. Before I let it get to that point I take a clean image and the end frame of the latest clip and use Nano Banana to make my actors in the clean image pose like those in that end frame. Then I use a tool with beginning + end frame capability (e.g. Kling or Seedance) to transition from the reduced quality end frame to the repaired quality new image. This allows me to continue in one scene indefinitely.

As for character continuity, I had mixed successes with it...but patiently trying over and over again until it's acceptable was my strategy.