Right now you can only re-look at the privilege token for a district if you place another merchant in the district. Well our group is not a big fan of memory games, it really favors the players with the better memory (usually the younger ones, I had quite a sharp memory in my 20's, not as great in my 40's, it's filled up more ).
So the variant is simply that as long as you have a merchant in the district you can secretly re-look at the privilege token for that district. Making it only on your turn will make it more controlled (not more than one hand on the board at a time).
This keeps the more important mechanic that only those who have already placed a merchant in the district get to see the priv token, but removes the needless memory aspect.