Thanks for a good answer! I had actually tried both of these (individually) with the same error:
import java.util.*;
import java.util.LinkedHashMap;
I had also tried restarted Processing but had not rebooted my system until today. And… now it works!
Addendum:
Turned out that what I wanted was best served by a custom class, since I needed key-value pairs but also an identifier that I could use to group them. In many ways, a class is simpler than remembering all the different nomenclature for maps and composites.