I don't usually do this, but I was digging on this Corpo Mente record when the Dulcin track startled me a bit...this perfect blend of acoustic guitar and heavy electric.  Plenty of bands and songs do this, but the particular sound I've been looking for has been elusive, at best.  This song captures almost precisely what's been in my head, in terms of sound.  I want this.  Bad.  Ha ha.  
 
I know it's not magic, but what do you all think is the best approach for this particular acoustic guitar sound?  If you listen through the heavy part, less than a minute, the heavy electric mutes and you hear the acoustic by itself.  Radiohead had a similar sound on OK Computer. 
 
The electric side, I can deal with that, but capturing acoustic guitar has always disappointed me.  I use the heavy strings, like they recommend, I angle my SM57, it's only 8 to 12 inches away generally, yet I'm cranking up the pre-amp to max just to get an acceptable level...it's been a challenge.  The sound I'm hearing on this song sounds more like super light strings, no thumping sounds when strumming and plucking strings.  
 
https://youtu.be/96EeSx60gYw?t=1487

Try a condenser mic instead of the 57.
 
Also, make sure you are picking up some of the body of the guitar.  If you are just picking up the strings at the 12th fret, it will sound thin.

that sounds like a typical gibson j-45 type or Guild flat top, with not too bright strings,
played in front of a nice condenser, thru a smooth tube pre, and with a healthy dose of 'just right' compression.
mic positioning is key.
with my big taylor, i point the mic at the point where the neck joins the body, at the fretboard..
and if i'm double micing, i'll point another towards the tail of the guitar, but not near the hole.
 
a perfect front end for this would be large or medium condenser, tube mic pre, outboard compression (set gentle), into a good converter.
 
you are right, not magic, but you will not get that sound with a 57.
 
i have posted lots of tunes of my own, with a similar kind of blending...
 
 
there are two approaches i use...
two tracks each of elec rhy and acoustic rhy,
played as tightly as possible (unless in my case, you WANT it loosy-goosy)......
and then you decide which is dominant....
pan the less dominant parts hard left and right, and pull them back in the mix,
then bring up the dominant parts, panned 50% left and right.
automate the volume and panning, and move them in tandem at will.

batsbrew
that sounds like a typical gibson j-45 type or Guild flat top, with not too bright strings,
played in front of a nice condenser, thru a smooth tube pre, and with a healthy dose of 'just right' compression.
mic positioning is key.
with my big taylor, i point the mic at the point where the neck joins the body, at the fretboard..
and if i'm double micing, i'll point another towards the tail of the guitar, but not near the hole.
 
a perfect front end for this would be large or medium condenser, tube mic pre, outboard compression (set gentle), into a good converter.
 
you are right, not magic, but you will not get that sound with a 57.

 
Well...I have a KSM27 condenser, which isn't bad, but then it feeds into an Art Tube Pre, which is a low budget pre-amp for sure, then into a Behringer compressor, another low budget box, then into a decent converter on the Onyx Mixer over Firewire and into the DAW.  
 
That's as close as I can get, for now, and will do some sound testing tonight and my recording-day-off tomorrow and see how close I can get.  
 
I want to be particularly careful with the compression.  I think I've set it too hard in the past, creating that thick-pluck sound I hear in my tunes.  It's almost percussive, and quite unattractive.  And I'm sick of it.  
 
I'm going to start with your advice here, and on the mixing and get this figured out.

you will want to go easy with the gain on the ART... don't hit it too hot.
keep it cleaN.
 
then when you go into the compressor, set the compressor for no more than 2:1, and no more than about 2-3 db compression...
go for a longer attack (about 40ms) and let the release be to taste (as fast as 20ms, as slow as 150)....
the idea with the compression on TRACKING, is to only knock off just a bit of level....
almost not enough to hear.
but it's there...
and later, on mixdown, apply more compression to suit the color of the track, and the way you want it to sit.
 
never try to do it all at one stage.
that's when you get the results you got.....

You might also try recording the DI from the acoustic piezo(if you have one). Then try using some acoustic guitar IRs(impulse response) on the DI. They aren't too expensive, IMO sound good and if it doesn't work it doesn't waste much time or energy. Just use your mic as usual and then  after everything is set up plug into your guitar and open a new track in Sonar. Afterwards you can decide which sounds better, your mic'd track or the DI track with the IR.
 

 
 

batsbrew
you will want to go easy with the gain on the ART... don't hit it too hot.
keep it cleaN.
 
then when you go into the compressor, set the compressor for no more than 2:1, and no more than about 2-3 db compression...
go for a longer attack (about 40ms) and let the release be to taste (as fast as 20ms, as slow as 150)....
the idea with the compression on TRACKING, is to only knock off just a bit of level....
almost not enough to hear.
but it's there...
and later, on mixdown, apply more compression to suit the color of the track, and the way you want it to sit.
 
never try to do it all at one stage.
that's when you get the results you got.....

By the way, just wanted to let you know this worked out really well.  I did, actually, achieve much of that sound I'm looking for out of the acoustic this weekend using your approach here.  Still need to practice some more on the finger picking part or I'd post it. The strumming stuff sounded terrific, light and sparkly, but still retaining the body of the sound. Something about recorded acoustic guitar just sounds so effin sweet...  
 
Definitely a large part of my issues were trying to do too much compression at tracking.  I learned my lesson.  Thanks!

Everyone's got a preferred method, and speaking for myself only, love to throw out suggestions...
Definitely use condenser microphones for acoustic. Also if u have, record the guitar pickup.
I record at least two condensers set at 45 or 90 deg off each other, my fishman matrix pickup into LR Baggs acoustic DI (can't get a better DI IMHO), then have a dynamic microphone in front of my CybertwinSE which is in a different room.

I go for having as many source tracks to use later when mixing and trying to get the fullness of an acoustic guitar in a primarily acoustic song. I've found adding together different sources at different times provide meat for a final track.