I tried the running section (back section) from an old weight forward line. That was probably the best.
Plain mono, around 20#. I could make it work, but.....
One Tenkara guy, Charlie Stewart, I think, suggests 14# or 18# flouro line, which is denser and thus casts better. I have not tried it.
The furled Tenkara line has a nice weight and taper to it which casts well and gives a very delicate presentation. For dry flies, it's really the best, IMHO.
For dedicated nymphing, the running line above would be fine, especially with bead head and other weighted nymphs - cuz you're closer to throwing the weight of the fly rather than the line. In the usual mixed situation, I like the furled line just fine.
All the above were on a Tenkara rod. The panfish rod just felt awkward with anything. If I had to use a panfish rod, I would probably go with the running line.