So my question is if there is any way to tell whether image fuzziness
is a result of the scope or of the environment without looking through
a larger scope. In other words, how do I know if my scope's aperture
is the limiting factor?

Looking through other scopes is a good way to see if how yours compares.

But there are many variables as others have pointed out, collimation, cool
down, atmospheric stability (seeing) quality of the mount, quality of the
eyepieces...

And of course it depends on when you are viewing Jupiter. Right now Jupiter is
low in the early evening, so you are looking though lots of atmosphere and
muck. Got to wait until it gets at least 30 degrees from the horizon.

I see you are a fellow San Diegian. What part? I am in Clairemont and could
likely help you get your scope straightened out.

Best wishes, dark skies

jon