How to format text insets that break across pages?

I'm redoing an older book that has a lot of inset boxes. Here's a screenshot of a sample page in the original layout:

The original designer's rather clunky solution was separate text frames plus separate shades backgrounds. I'd love to find a solution that would allow me to keep one continuous text flow: The inset box anchored in the main text frame and flowing along with the rest of the text. Trouble is, I can't make either a single-cell table (which would otherwise be ideal) or a text frame anchored in the main text work across page breaks.

I'd like it to look more like this, but I've had to arange things here manually:

Hope the question makes sense!

~Valerie