As there's no answer yet, I started spending a lot of time at the Global Trade HQ. So far, I've increased my storage capacity from 260 to 280, bought one land expansion and two beach expansions, and purchased as many lanterns and lucky cats as I could to build Tokyo town zones, so that I went from 35 to 21 bonsai trees. Unfortunately, I've thus leveled up to 23 and have two new item categories in the storage. Besides, I had to spend almost all simoleons in the process and have only 13,000 left.
My current strategy is to buy the last piece of beach area, and then get rid of all beach expansion items. After that, I'll go for the remaining 11 pieces of land (which will of course take a while).
However, I'm still interested in hearing what others are doing to use their storage efficiently.