How do you play this (guitar question)?

This is part of a tab from Simon & Garfunkel’s “Anji” (off of the Sounds of Silence CD). I am wondering what the best way to play the areas marked by the “x”. I have tried holding my index finger across the strings (like a bar chord) while not actually pressing the strings all the way down. However, I don’t exactly know where the finger is supposed to be (I usually just place it over the 2nd fret by default). I’ve also tried placing my non-index fingers on the strings with the same half-pressure.

In any case, I can never get it to sound like the recording, so I’m probably going about this all wrong. I’ve noticed that using a pick with this effect sounds better than fingerpicking (which is too bad, since I fingerpick this song), but they both sound off.

Any tips?
||------------|---------------|-----------------|--------------|
||------------|---------------|-----------------|--------------|
||-2----------|-------------0-|-2---------------|----x---------|
||-2--------0-|-0h2–2-0h2----|-2---------------|----x---------|
||-0—0h3----|---------------|-0-----0h3p0-----|-0–x---------|
||------------|---------------|-------------0h3-|----x—0h3h4-|

|-------------|---------------|-------------|—0-----0—||
|-------------|---------------|--------1----|—3-----1—||
|----x--------|-------------0-|-x------2----|—2-----2—||
|----x------0-|-0h2–2-0h2----|-x------2----|-------------||
|-0–x-0h3----|---------------|-x-----------|-------------||
|----x--------|---------------|------x------|-x-----x-----||

I don’t know how Paul Simon did it but I find that I’m just holding my index finger at the second fret (basically holding the A chord) and damping the muted notes with my middle finger. In the last two measures I damp the muted notes on the E string with my thumb.