Unless the save is loaded twice in a row, game crashes on save.

[Ramagast]

So, a year or so ago my Skyrim developed a problem with saving games. It was random - I'm starting a new game with a fresh install and a new, clean mod setup, playing it for 20-40 hours without problem and ten BAM! The game crashes on save. What was weirder, I was playing, say, for two hours, creating saves left and right, no problems at all. Then I would leave the game. return to it on the next day, load any of these saves, including earlier ones, and after loading it any time I wanted to save again, the game would crash.

Now, I know my way around modding somewhat - I was here since Morrowind. I understand load order, follow all installation instructions, read descriptions and posts, can see the reasons for most bugs, can create my own compatibility patches in TESEdit, generate Dyndolod, fix the grey face and so on. I never uninstalled a mod during a playthrough. I checked my saves with ReSaver and there is nothing wrong with them: no unattached instances, no active scripts overload, nothing. The game runs fine, it just can't create a save game for some reason. It's not a question of save size - I'm running Engine Fixes with "SaveGameMaxSize = true" and my saves aren't this big.

After half of year of rebuilding my mod setup, reinstalling everything, trying dozens of mod combinations and failing, again and again, I found one advice that worked for me, weirdly: "Load your save, then immediately load it again - and you'll be able to save your game in a new slot". And it worked! The problem is, I'm now forced to do it each time I'm launching my game and I can't help but feel that it isn't healthy. Skyrim has a lot of talk surrounding its save system, and while some of it can be superstition, I've always tried to follow the advice - "don't use quicksaves or autosaves", "don't just load your game if you're killed - quit, launch Skyrim again and load it from a main menu", etc.

So, while my game isn't completely broken (at least, according to ReSaver, it's still fine), this situation worries me more and more.
Anyone else encountered it?
Maybe someone knows the cause of it (what's up with the need of double loading?) or the more permanent cure?

I'm not attaching my mod list as it's really big, and during my experiments I've changed it a lot with no effect on the problem. If it was some mods fault, it would be wildly known by now.