Cooking for longer on a lower power setting will still save your food from being an over microwaved mess even with a better dish to cook it in. Lower power for longer results in more even heating across all the food and tends not to dry things out so drastically.

Can you recommend something? I mostly I use crockery plates or glass containsers, which work, but can get pretty hot.

Or just get an air fryer. Most things people make in the microwave can be made in an air fryer, and it almost always comes out leaps and bounds better.