@ELD Man, thanks again for following up on this. By SSHing into the vagrant box and running the artisan commands from inside the box rather than on the command line in the directory from my own machine, it finally worked!
Maybe this was one of those obvious times where everyone knows commands won't work unless you've SSHed into the box first, but everything else worked, and it worked using both sqlite and mysql DB_CONNECTION options.
So, to recap: If you are using DB_CONNECTION=pgsql and you try to run php artisan migrate or php artisan db:seed from your main command line, you will get an error message of:
[PDOException]
SQLSTATE[08006] [7] FATAL: role "homestead" does not exist
When this happens, you need to go to your homestead installation directory and type vagrant ssh. This will get you into the vagrant box. From there, you can verify that postgres sql is running with the command
psql -U homestead -h localhost
Once you have verified that, navigate to your app's directory and run artisan commands as normal, such as php artisan migrate and php artisan db:seed
Thanks to @ELD for debugging and explaining how he was able to make it work. Good luck to anyone else with this issue!