Hey Brian,
Not sure on the exact setup you are on (Migrating from block list v13 to block list v17 for example or from an older property like nested content on v13 to block list in v17) or if you have access to Umbraco Deploy.
But what I experienced in the past that tended to cause these issues was that the JSON Data from within the block grids and lists was not getting a new bit of data attached to it called the “expose” object when it was transformed as part of the upgrade.
Its effectively what tells the block grid and list what parts are published and in what language (In a very simplified manner of explanation).
I wrote up some code that I posted on the issue board at the beginning of the year in deploy: Migrating Legacy Grids to Block Grids and Nested Contents to Block Lists misses the expose value. · Issue #325 · umbraco/Umbraco.Deploy.Issues · GitHub
Might be worth a look to see if your “Post” migrated block lists / grids contain that expose value and if not, attempt a migration to try and include them?
Fair warning, the code I wrote in the attached issue hooks into the Umbraco deploy artifact migration flow, so if not using deploy, you would have to rewrite it appropriately to however you prefer to do the content migration.