For your example, I suggest you go with your gut.
Further and Farther have been used interchangeably for years, even by the experts in English.
From Quick & Dirty Tips .com:
Wherever possible, use “farther” for physical distance and “further”
for metaphorical, or figurative, distance. It's easy to remember
because “farther” has the word “far” in it, and“far” obviously relates
to physical distance.
Sometimes it's hard to decide whether you're talking about physical
distance.
The good news is that in ambiguous cases it doesn't matter which word
you choose. Although careful writers will try to stick with the
distinction between “further” and “farther,” the _Oxford English
Dictionary, Fowler's Modern English Usage_, and a number of other
sources say that, in most cases, it's fine to use “further” and
“farther” interchangeably, especially when the distinction isn't
clear. People have been using them interchangeably for hundreds of
years, and a few experts don't even follow the distinction.