Combine items from multiple boards into a single board with a different grouping structure

I have four marketing teams, each with their own boards. The boards are used to plan/track programs, where each program is an item in the board. For all intents and purposes, the column structures are identical. They do have two different grouping structures - one by program status, the other by fiscal year/quarter.

What I am trying to accomplish is a way to create a main board that contains every item from all three boards, keep them in synch and, regardless of how they are grouped originally, group all the items by fiscal year/quarter.

I’ve tried all kinds of workarounds, but, I keep stubbing my toe.

My point of view: I’m trying to look at each of the four existing boards simply as “data sources” to populate the new board. I’ve tried mirroring all the columns, but, then the lack of full support of mirrored columns in automations becomes a problem.