I don't know if it's still relevant, but I think I have found the reason for this bug (or at least one possible reason that causes it). I forced Oblivion to an unusual resolution to get rid of unproper stretching while playing it in VR (I use my own concoction to play in VR: TriDef for stereoscopics, Kinoni Streamer or TrinusVR to stream it on my Smartphone (Android Phone) and if I use the Kinoni Streamer I additionally implement ReShade for a Barrel-Lens-Distortion). When I try to quicksave, autosave, console save or menu-save while using this unusual resolution, the game crashes (CDT). Always. If I use standard resolutions like 800x600, 1280x720, 1920x1080 the game saves perfectly fine. I tested it now several times, it only happens with resolutions that are not native to the game (even ingame resolutions like 720x576 may cause this bug while in window mode). I forced Oblivion to this unusal resolution by changing the corresponding values in the Oblivion.ini (to be found in mydocuments/games/oblivion/oblivion.ini; the resolution values are located under the "display" section). It actually worked as I hoped it would in VR, unfortunately I can not save or load anything in this resolution, so I guess I have to find another way to solve the stretching problem in VR.
So it's probably the resolution of your game that causes the save-crash (either by accident or on purpose via an installed mod). I suspect the resolution gets saved along the character stats and creates a conflict with your currently running game and crashes (that's probably the reason why even a successful saved game causes a crash when loaded back up - if the loaded resolution creates a conflict with the resolution that your game-session currently runs with). So better make sure not using any mods that meddle with the resolution (including graphical overhauls). I suggest to keep the game resolution at standard values (ingame values provided via the launcher).
Speculation: It is possible that the resolution save-crash issue isn't the only reason that triggers the quicksave CDT bug. It could very well be the case that any form of conflicting information (like RGB values, Chroma/Luma (Gamma) values, postprocessing effects, etc.), of which the base game is in conflict with, causes this bug. But the resolution problem described above reliably produces said quicksave CDT bug (without exception) that you guys experience as well.