I did a couple of quick jammin run throughs just to show you that you can get quite musical with just one finger. I did add a third finger here and there at the same time to add a bass note, could have used just one only moved it faster or a thumb over. I snuck up to the D chord at the 10th and hit an A7 on the way back down to the A minor chord. Fooled with the first 3 notes of the C chord down at the nut, passed through 2 notes of the D chord that lined up on the way back up to the G chord.
As you can hear, there are ways around your limitations once you know where the intervals are. It doesn't matter how many strings your fingers cover, one or four as long as they are the ones you want. Just don't pick the notes you don't need.
I could play through that 1/2 a dozen ways just adding different notes from different chord positions and supporting notes all over the neck without too much effort.
The notes are all there under your hand just waiting for you to find them. Look closely at the
Caged system or pick up Kirk's book, Plain Talk. A fast way for you to map out the fretboard which is key for you since you will have to find your own unique way through a tune.
Hope this helps bro.