It’s very difficult to reach from frets 1 or 2 to frets 7 or 8. You can manage it on the mandolin because the mandolin’s 13-inch scale means that you can place the index finger on the 2nd fret and the pinky finger on the 7th fret without too much trouble. But even on a 21” scale tenor banjo that just isn’t doable. So what if you added a 5th string and tuned in 4ths? That might be a good compromise.
A 5-string instrument tuned in straight 4ths A-D-G-C-F would have a similar pitch range, but everywhere requiring stretch from frets 2 to 7 on tenor banjo would only be from frets 2 to 5 in 4ths tuning. The next fretted note in the scale would always be on the 2nd fret of the next higher string and not the 7th fret of the current string.
I haven’t given too much thought yet to the chord shapes, but from a melodic standpoint single-note melodies should fall under the fingers pretty well in 4ths tuning. Since you would not have to use any open strings, transposing a melody to another key would be as simple as taking that same pattern and moving it up or down the neck. This might allow you to perceive melodies like a horn player.
I am going to try this out with an inexpensive short-scale Luna guitar. A local luthier is going to set it up as a 5-string left-handed instrument tuned in 4ths – A-D-G-C-F – using a mandolin tailpiece to keep the strings low to the body behind the bridge saddle. We’ll see how it goes! I'll report back once I've tried it out.