Have you considered the
Verso Wrap Light by Lightwedge?
Haven't tried it myself, but it looks like it might fit the bill.
They ain't cheap but they're rechargeable via USB and have clips to mount to a variety of bezels. Marketing fluff even says they'll fit on the the Pocket (not sure if they mean 350 and not 300). Lightwedge -- for their excessive prices -- can make good booklights.
Whatever you settle on, let us know!