Translating "Jii-san" as "Grandpa" actually makes sense. Personally, I've always understood "jii-san" to means "gramps" and being very informal, and that doesn't quite feel like the relationship they have (yet), but at the same time "Grandfather" feels too formal, so you really are kind of stuck.
You know what? I like "Grandpa." It can still be used more informally, as between friends, and that's more like the relationship the two have, versus the Elder and his granddaughter, which is still more formal as befitting a regal lineage.