I also follow a diet of 'real food' that is simple and unprocessed. I also struggle to meet my calories every day because I stay full, but I also make sure that I'm completely nourished. I choose foods that are nutrient dense to make sure that I get everything I need. And like you, I also don't follow a regular eating schedule
I use a nutrition program that tracks about 40 nutrients, and I meet or exceed the RDA in everything - even with minimal calories. I lost a lot of weight with this plan and maintained high energy levels.
Regarding eating more even if you aren't hungry, I would suggest it if you haven't met your daily requirement of nutrients or if you lack energy. Also keep in mind that most apps are not very accurate when it comes to suggested calorie ranges, so it may be asking you to eat more than you need. However, if you can eat the suggested amount and still lose weight, then you should stick with it