I am supplementing the bug report with new findings. I also tried to break the record for Chaos Mod and Ultra Chaos Mod and found that they also have the same problem with recording the results.
Chaos Mod - Faster 7:10
Ultra Chaos - faster than 7:30.
At the same time, it seems that the problem arises not with recording a record, but with overwriting it. The new result is simply not updated in the high score table when you exit the menu. In the case of the ultra chaos mod, my new record was only about 14 seconds faster.
Also, after playing with the settings, I discovered how poorly changing the resolution of the game works. Changes are made either after restarting the game, or when switching to full-screen mode, or they are not made at all. I think this problem also deserves your attention.
Eventually, I managed to get my resolution settings back by restarting the game and trying to change them again.