When I'm playing a song with a lot of minors, sometimes I'll just drop the third in the tuning (that doesn't seem to work for G tuning, though).
Otherwise I just avoid the third interval, which is second string in G tuning (D-G-D-G-B-D),
Right now I'm working up a song in G that has Em and Am in the progression: I solved that by playing a two-string lick for Em with the open B and the tilted slide at the II fret on the D string, so I get an E/B combination without the third, which works pretty well. For the Am (in this song it comes right after the Em) I level out the slide and pluck the G and D strings at the II fret, which gives an A/E combination (again, no third) and passes for a minor.
Another place to play the Em is at the IX fret, picking the D and G strings for a B/E two-string chord. This is where you hit the Em in Running On Faith, since you're going back and forth between the V, VII and XII frets.
I've played for years in open E, and for songs like Dylan's You're A Big Girl Now I tune to Em (we play the song a semitone flat, compared to the recording) which gives me the minor third; this is necessary in that song, since it has a strong flavor of the minor and you can't easily get by just by avoiding the third.
Back to setup: I no longer play without the slide (except, of course, when I'm playing bass) but over the years I have adapted my touch to everything from a pedal steel to my Les Paul with pretty low action (but not really light strings: I use .011-.049 with a wound 3rd). I go back and forth between a high-action Dobro and the LP in the course of a set, and it's really just a matter of learning the touch. I don't think the tone is particularly enhanced by having a big honkin gap between the pickups and the strings.
I can dig in a lot harder on the Dobro, but that's the way it's supposed to sound. I like the glassy, Duane Allman tone on electric, not the crash/bang style.
Anyway, I use open tunings exclusively, a decision I made many years ago when it became obvious that I stand on Main Street, throw a rock, and hit five guitarists better than me. I decided to concentrate on slide, and it's getting where it's working pretty good. BTW, you mentioned pedal steel: I had one for a few years (traded it off after foot and knee surgery made it impossible to play) and it sure made me smarter when it came to figuring out intervals on the six string.
The essential difficulty with open tunings played with a bottleneck or steel is that you're stuck with its intervals, until you figure out how to sound like you're not!
