Being mindful of your strumming is a great advantage. There are probably a few things that you are doing and as @judi said, it will get better.
- The depth of the pick below the strings doesn’t need to be much
- The amount of pick protruding from your fingers could be too much - I have reduced that in my time learning. Dig around for “holding the pick” on the forums here.
- You will eventually develop a little rotation in your wrist. This helps the change between up and down strums to be fluid and glide across the strings
- The direction the pick strikes the string will determine much of the rotation you are getting. If the edge is hitting before the flat, you will get some rotation. You may want the edge later, but for strumming, I really try to use the flat and then rotate my wrist a little so it doesn’t dig under the string. - i may need pictures. if I do, let me know.
For me, I struggled for a few months and then, seemingly overnight, it just worked. Fairly fluid and I could strum with super stiff picks. I still prefer some flex, but not the super flex nylon that Justin recommends in the beginner class. I tend to grab the orange Tortex (0.6mm) at this point for strumming stuff.
Some good info here: How To Hold A Guitar Pick