I see it a lot brighter now, so I'd like to give some hope to you, too. Firstly, with the amount of cases, the words "planned obsolescence" need to be dropped here. I cannot believe the immense efforts apple seems to go to not acknowledge that this series of iMacs has serious issues. Also, not at all replying to this gigantic thread made me get to the decision to leave apple products forever after using them exclusively for my whole life even before they were "cool". If some manager reads this, this is your doing and I will keep telling everyone I know, that Apple sells faulty (expensive!!!) products and does not stand by it but chooses to ignore their customers.
Sooo, now the advices:
I talked to someone on reddit with the same problem and he did some research: People that replaced the power supply are mostly happy now. The problem seems to be, that even the licensed workshop I'm going to because I lack any AppleCare does not simply want to replace it. They want to diagnose the problem and then make me an offer. 😟 Soooo, if you get your people to replace the power supple, then there is a chance you're fine, but getting them to do that might prove difficult. I'm very close to getting the parts and tools and opening that thing myself since, as you said, it's basically useless now.
As a short-time solution and kind of troubleshooting: Try disconnecting your iMac from power completely everytime it is shut down (especially during the night) and you should experience much longer uptime. If not, there might be something wrong with the mac outside of the power supply. So far it worked quite alright for me.