Maybe try posting a video of what you’re struggling with? Ideally a song, or excerpt from a song, so it’s while playing. It’s harder to analyse just in text.
Learning to adapt chords and playing to your strengths and weaknesses is a real thing. Thinner fingers have some advantages and some disadvantages.
Maybe a photo of how you play it? Are you doing finger stretching exercises (on the guitar) as well?
If I’m playing 3 finger A, I end up muting the high E if I try to mute the low E. 1 finger A is easier to mute the low E with. D though, that’s going to depend on hand size. Initially I couldn’t mute the low E, now I can mute it or fret a bass note. I would guess my hands are larger than yours though (although I do not have big hands - my wife’s fingers are as long as mine).
I would continue to try to mute with the fretting hand. Strumming hand muting is different and wouldn’t work for a big strumming song (or at least you’d use it for a different sound). In order to mute the bass notes with these chords you do need to grip the neck deeper with the palm of your hand. It’s a different finger grip.
I get that. Some barres are more comfortable than opens once you get proficient at them.
I think you really need to record yourself playing. Even if you don’t post it! It gives another angle to analyse what you’re doing, and then compare with what you see others doing on YouTube (e.g. Justin).
Hah, yes, sometimes. If a chord is at the limits of my hand flexibility this happens. When fretting a chord, I think your hand should be relaxed - once you’ve learnt it, as often during the learning process it’s tense. Working on hand flexibility helps this a lot.