Thank you all for the thoughtful replies, critical listening, advice, etc.

Points well taken that there are multiple effected things going on - I'm not going to be able to cover all of that by my lonesome.

I am also aware that it's not my job to duplicate exactly what I hear on recording, but if you hang with me long enough, I take that on as a personal challenge. If I can get close, I'm going to do it.

I should also say that I've always wanted to learn slide on electric, and this seemed like a good excuse to go drop the 10$ to buy a slide, but I've held out in the past for one of those fancy 'flip the lever' slides like this: JetSlide at Musician's Friend but I've never been at a shop that has one on hand to see if I can make the lever thing work. Ring slides intrigue me as well like this one: Shubb Axxys

Here's what I do have going for me - I have a patch already in my Zoom G5, with a really long attack on the compressor and nice sustain - it feeds a delay which actually does octave harmonics on each successive feedback, then feeds a big hall reverb. It volume swells nicely on it's own, in other words. No pinky action on the volume knob (though I've been there before) The G5 also has a pedal which you can program for volume swells, but it's travel is pretty tight (one of my only complaints with the unit), so I rely more on the patch than the pedal for volume swells. It's a very purty pad that results out of it.

But, it's not going to sound slide-y like on "Beautiful". I might just get a cheap pinky slide to see if I can get close on the tone. I'm thinking neck humbucker, tone turned about halfway, with a Fender Deluxe Reverb for the amp, with minimal dirt. Slow attack on the compressor ahead of the amp, with delay and reverb following the amp as a starting point for the patch.