I tried 4.1-mini and 4.1-nano. The response are a lot faster, but for my use-case they seem to be a lot worse than 4o-mini(they fail to complete the task when 4o-mini could do it). Maybe I have to update my prompts...
I will check again the prompt, maybe 4o-mini ignores some instructions that 4.1 doesn't (instructions which might result in the LLM returning zero data).