I'm using GOG version 3.6.69.4648 on Windows 10 64-bit.
I have tried the various fixes posted online, including:

> disable cloud saves
> run Verify/Repair

I also re-installed from scratch, since my previous version of DOS2 was old.

But still, I crash with the Error 503/504 issues when I try to Quick Save.
Normal named saves seem to work fine.

Is there any other known way to fix Quick Save with this game?

//*****************************************************************************
Later note:
Okay, I found another solution which *does* appear to have worked:
basically, go to:
C:\Users\<username>\Documents\Larian Studios\Divinity Original Sin 2 Definitive Edition\PlayerProfiles\Gorlash\Savegames\Story
And delete all of the existing QuickSave_NN directories.
After this, Quick Save appears to work now...

//*****************************************************************************
Even Later note:
However, even after doing this, once you've created all specified number of Quicksave files, the saves will start crashing again, and you have to go back and delete all the Quicksave directories again. Apparently, the current version DOS2DE does not know how to delete directories/files under current Windows 10 version.

I also have been having the same crashing with Autosave, once *those* get up to 16 (in my case) copies... solution there is the same; delete all the Autosave directories.