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Hello @flagguy ,
It’s true there are several different ways to play a G chord, but no matter which 2 fingers are fretting the 6th and 5th strings, the answer is the same. The problem is that the finger fretting the 6th string is too flat and is touching the 5th string, thus partially muting it. It is necessary to push your wrist forward and lower you thumb to the middle of the back of the neck so that you can get good arch in your fingers. Then, it is important to fret the string with the very tip of your fingers, not the fleshy pad.
Good arch and finger tip are the answers to the problem you are having. It may take some time and some experimenting. Go slowly and take deep breaths often. And stretching will help a lot as @the-old-coach has suggested.
Now, in your description, you mentioned the A string and the high E. The A string is very easy to understand. All I can assume with the high E is that you are using your pinky and because it is so small, you are having trouble accurately fretting the string. Again, this will take time. Go slowly and take many deep breaths.
If you will be patient and persistent, you will get it. The biggest problem is to have fun while you are going through this phase so that your motivation to play guitar continues to be strong. So only spend a few minutes at a time working on your chords. You can do this every day and even several times a day, but don’t wear yourself out. After working on your chords, focus on making some pleasing sounds on your guitar. Have fun doing this. Do this after every single practice session so that you learn to love your sound, the music that flows from within you.
MG 😀