This is definitely something that affects any beginning marching snare drummers. I'll offer an exercise that may aid in making you more comfortable with your grip in relation to rebound as well as help you with proper left hand rotation and build your left hand wrist chops. DISCLAIMER: This is best done on a real drum.
So, as you said, take it back to basics.
-First Step of exercise
1. Hold your hand out (no stick) in playing position. For this your hand should be flat and fingers spread and extended. Check that your hand is in line with your forearm.
2. Start to slowly rotate your wrist as if you are playing, wrist still in line with forearm and fingers still spread and extended. You should see that as your hand rotates, one finger remains still (the axis of the rotation). This finger SHOULD be your middle finger. If it is your pointer finger, your hand is pointed too far down. If it's your ring finger, your hand is pointed too far up. If your wrist is in line with the forearm and your hand is rotating around the middle finger, congrats! This is the first step to proper left hand rotation, allowing for maximum rebound by later moving the stick straight up and down.
3. Start to speed up this rotation until you can consistently keep the rotation around the middle finger.
-Second step of the exercise
1. Grab your stick and place it into the fulcrum (about 1/4 to 1/3 of the way down the stick depending on the type of stick). At this point your fingers should still be extended.
2. Begin to just play legato strokes like this. Aim to keep your forearm still and use only your wrist to move the stick down, but letting the stick return to the top of the stroke by rebounding. Careful not to push with your thumb to move the stick. This is all about the wrist. Your thumb may begin to hurt a little, take a break, reset the stick, and continue.
3. The next step is (contrary to what may be your first instinct) to add your ring and pinky fingers (keeping them connected to each other like one big finger). With this I'll introduce the concept of "contact without pressure". The ring finger should remain contact with the stick as often as possible, but you should not add any extra pressure to achieve this. This is for control while still allowing the stick to move as it wants to with rebound. While still playing legato strokes, begin to slowly add these fingers and remove them. Try to make the rebound feel the same as you slowly add and remove them.
4. Once you are comfortable with those two fingers, leave them on and do the same process with your pointer finger, trying to make the rebound feel the same as you slowly add and remove this finger.
5.Once you are comfortable with that, do the same with the middle finger. The middle finger, like the ring and pinky, is more for control. Again think contact without pressure.
The point of this process is for you to learn what each finger or set of finger' job is in the traditional grip and let them do their job and only that and not end up hindering your rebound. Learning the traditional grip can be quite a task that can take a long time to really become proficient in, but with some effort I'm sure you'll be great! I hope this helps!