This article has been deprecated.
Thank you to all the people who have read this article over the years, or to those who have linked to it - the amount of traffic was quite surprising.
Unfortunately the solution no longer works reliably (due to updates from both Synology and Resolve. Note: the article was almost 5 years old).
I have therefore removed the article in its entirety. I apologize for any inconvenience this may cause.
Should you still need to look at the old video, I have an unlisted version available here:
If DSM borked up your Postgres again, you should be able to recover your data using the steps shown in this.
If you are looking for a solution to run PostgreSQL on a Synology NAS, I recommend you look at this project by Elliot Matson on GitHub instead.
If your Synology supports virtual machines, using that docker container on any VM will be your best bet without too much tinkering.
I will leave this page up for a while, but it will eventually be removed.