I have the same dilemma in situations when wearing a trench closed is impractical, but carrying it on my arm would be awkward.
(For example: I'm shopping on a rainy day and running in between stores that have outdoor entrances. The stores are quite heated so wearing the trench closed while inside is too warm, but I don't want to fuss with carrying it when I am also trying to pick up other items.)
Honestly, I haven't found a solution that works better in these situations than knotting the ends behind me. Leaving the ends loose seems sloppier, and the belt sometimes will fall out of the loops. Taking the belt off altogether would be fine if I did so at the beginning of the day before leaving home, but it's a pain to have to take it off and put it back on mid-way through an excursion.
I'll be looking at this thread for better ideas!