ichard was hard at work and created a foreign data wrapper (FDW) to access a cloned dolt instance and copy the data into our own PostgreSQL instance that our applications run on.
The current implementation is that Dolt fires information over a webhook when a branch is pushed / merged. We can use this information to see exactly when a PR is merged into master and trigger a dolt pull and restart of our dolt sql-server instance. Then, a stored procedure will activate to load the new data into our PostgreSQL instance so we always have a stable, up-to-date, local copy.