Read the actual
the Chicago code, to me it does not prohibit a feeder from supplying a SFD. Do your read that in there?
There a re extra rules in 560 if you have a service to a SFD.
You have a service to a garage which in code language is a 'residential accessory structure'.
From the garage to the single family dwelling (SFD) you have a outdoor feeder that falls under article 225.
Since you don't have a service supplying the SFD the code extra rules in 560 don't apply, simply the normal rules under 225.
If I am uncertain about a AHJ's take on a complex code rule what I do is submit a plan with my permit applications and request a 'plan review' instead of a 'over the counter' permit
Then if they reject my plan at least its not installed yet.
Hope that helps.