Chicago's brief is online
Pdf is here. Reading it now.
Thoughts after a quick read: stylistically, well-written. The argument against due process incorporation involves taking what the Court has said and not what the Court has done. The Court has said that "fundamental rights" are something of a narrow class of rights ... rights without which there is liberty or civilization. But what it did while so saying was to rule fundamental almost all the rest of the bill of rights, and unincorporated rights such as the rights to contraception, abortion, and gay relationships.
I think we can say that there can be liberty and civilization without, oh, jury trial for major misdemeanors, the right to buy condoms, the right to an appointed attorney. For that matter, with an established church, such as in England, and the right of the prosecution to move for a new trial based on legal errors. I vastly prefer living in THIS civilization and with THESE freedoms, but I can envision a liberty and civilization without them.
With regard privileges or immunities incorporation, it's right what we could expect. (1) Don't overrule 100+ years of case law and (2) OK, so there are quite a few mentions in 1866-68 of p or i enforcing the bill of rights, but they're not enough and not clear enough for our tastes. With a dash of (3) if you incorporate via p or i (AND use it to abandon rather than supplement due process incorporation) then you have to withdraw all bill of rights protections from corporations and aliens, since they may be "persons," but are not "citizens."