This is completely off the wall, but sometimes, just for the hell of it I play my guitar across my lap and chord with just my first two fingers, usually because I've been using a steel slide in a normal tuning. I can get by in E,D and G, and the significant difference in playing this "lap-dulcimer" style guitar is that it reverses the two fingers, ie it puts the second finger nearest the nut, so the more versatile index fingertip can bend backwards to form the chords. It might be worth a try.