I would like to get going with an installation of OpenEMR on a Synology NAS as well, similar to you.
I am happy to write up a small wiki for the community (I believe installation should be quite straight forward on Synology). Howverver, at the moment I get stuck here, similar to you: Synology OpenEMR Installation "stuck" at Step 3 - : unable to connect to database as root - #3 by PeteBoyd
Can anybody assist who has successsfully installed on a Synology NAS (DSM 7 with Docker)?