I got a response today - turns out they're not willing to sell 16m² abandoned parcels to anyone unless they have land adjacent to it.
That's disappointing but not super surprising. I guess I'll take a look at what 16m² parcels are for sale instead and see if there's any in a good position, for a price that's not ridiculous.
If there's none, I can either try to extend out the 48m² land I have or just stop caring that I have 32m² land tier left. I could use it if I upgrade to premium eventually.
Actually, better idea:
Instead of putting an ice cream stand somewhere with a 5 LI budget, just make a nice looking, bigger ice cream shop at my house.
It's really minimal but I think it looks great, and the plants on the gazebo fit Sherbet's aesthetic.
I'll want to set it up so that you can actually get ice cream from the display, which won't be hard.