use_remote_estimate isn't really a solution as it adds way too much overhead and processing time to every query run.
Maybe this is the thing which should be addressed. Can you quantify what you see here? How much overhead is being added for each query? Is this principally processing time, or network latency?
Since these tables are being continuously analyzed in the database that hosts the data, is there some way that they statistics could be easily passed through the foreign server mechanism to the remote database that's calling the query?
Since FDW can cross version boundaries, it is hard to see how this would work. Maybe something could be done for the special case of where the versions match. I think collations/encoding would be a problem, though.
What I am hoping for is either:
2. add the ability to automatically run analyze on foreign tables just as they are currently run on local tables.
That wouldn't work because communication is always initiated on the wrong side. But it should be fairly easy to script something outside of the database which would connect to both, and poll the "foreign" pg_stat_all_tables.last_autovacuum and initiate a local ANALYZE for each table which was recently autoanalyzed on the foreign side.