This system seems similar to the hairdresser that I go to. The type of haircut chosen on the website is what you have now as it gives the stylist a timeframe of how long it’s going to take. I have been told to choose the level that is higher than what I have just to give more time if needed. It also depends on whether you are just doing minor maintenance or a full style blowout thing. Considering you’re cutting off quite a bit then maybe taking the higher “level” will help.
If they get mad at your length then it is kind of their fault for stating “men’s haircut” on the site.