Just another follow-up as we got back from another few days in Seoul and used the Olleh Egg again.
The "egg" we got this time was a bit bigger (though still fits on the palm of your hand) though thinner with similar battery life.
Encountered a lack of signal within a few bars/restaurants we visited.
Saw some people at a few bars/restaurants, handing over their phones to the barkeep/waiter to charge.
Didn't make a reservation ahead of time and thus got dinged for an extra 3000W/day rental charge.