Well, for starters, the 5th amendment doesn't really apply to Congress as much as the Executive and the Judicial branchs. Congress merely makes the laws. The Executive enforces the laws, and the Judicial interprets the laws.
In the criminal justice system, violations of the law are prosecuted by the Executive in the form of police authorities and prosecutions, and the legal case is put to an impartial trial (Cue Law and Order "Doing Doing")
In the court room, there are two powers: Trier of Law, and Trier of Fact. The former is the Judge, whose job it is to set up the game rules of the trial and interpret the laws in question and what is needed to convict on any charges brought against the defending. The latter is typically the Jury, who determine if the evidence presented supports the Judge's interpretation of the benchmarks for conviction. At the request of the Defense, the Trier of Fact may instead be the Judge himself (A Bench Trial), who will make the determination. The prosecution has no right to request this or contest this.
Once the law is created, Congress has little say in the process. Judges in the US are notoriously territorial. If Congress or the Executive (or anyone, really) tries to tell them how to run their court, they will tell that group where they can stick their "rule". One quite notable instance, a case before SCOTUS on Affordible Care Act, then President Barrack Obama insisted the court must rule in favor of the act. SCOTUS responded by holding off on releasing the decision until Obama wrote them an essay on the nature of the Checks and Balances of the Three Branches of Government according to the President (Petty, yes. But it got the point across: "Don't tell us how to do our job").
Judges are mostly administered by the superior court they fall under, with the Chief Justice of SCOTUS administering the U.S. Federal system. Congress can impeach a judge for misconduct but rarely does so. Judges will typically have long terms OR life time appointments to prevent the political nature of running for elected office from introducing bias into the court (often recusing themselves if it appears they could be biased.). Typically, violations of the 5th amendment are handled by the judicial system through appeals to superior court who will review the case to ensure the Prosection and the Lower Judge followed the rules. The abuses violating the 5th Amendment (as well as search and seizure and right to council) are going to be abused by the enforcers and interpreters of the law, not by congress.
This doesn't mean Congress can't write a law that allows for the such abuses to happen, but that doesn't make it a legal law and it gets overturned by the same chain of judges declaring it unconstitutional. Rather, any party can be guilty of this.
Conversely, with the First Amendment, writing laws is the sole responsibility of Congress, so naturally, if there is a law saying they can't make this law, in a working system it shouldn't hit the Executive's desk at all. When such a thing does, the Executive is sworn to uphold as best he can. Judges again being territorial, have read previous case law on similar matters, so they would be aware that in American Jurisprudence, speech is considered Protected Speech until proven otherwise (its a hard criteria too), so any enforcement of law before a judge is going to have to prove that this is not Protected Speech automatically before they can proceed further (if you ever read some free speech cases, they are almost always 9-0 or 8-1 in favor of the speaker.).
Has the Supreme Court ever used the difference in wording between the 1st Amendment and other amendments to decide a case? In particular, cases between the 1798 passage of the 11th Amendment and the 1868 passage of the 14th Amendment?
To the best of my knowledge, no.
Only a handful of cases invoked the First Amendment as an individual right prior to World War I and that was one of the first provisions of the Bill of Rights to be judicially enforced.
In particular, did any part of the Supreme Court's https://en.wikipedia.org/wiki/Chisholm_v._Georgia decision rely on the different wording in the amendments? I realize the 11th Amendment effectively invalidated this decision, though the later 14th Amendment largely annulled the 11th Amendment, at least in my opinion.
No. The full text of the opinion is here.
Currently, does the Supreme Court regard the Bill of Rights (excluding the 1st Amendment) as apply to the States because of their wording, because of the 14th Amendment, or is the issue largely moot now?
The U.S. Supreme Court regards most of the Bill of Rights including the 1st Amendment as applying to the States under a doctrine called selective incorporation that engaged in an analysis under the due process clause of the 14th Amendment.
The most recently incorporated provision of the Bill of Rights was the Second Amendment. McDonald v. City of Chicago (U.S. 2010).
The most notable rights not incorporated are:
The right to a unanimous jury of twelve from the state and district where a crime occurred in a criminal case (smaller juries and non-unanimous juries are allowed in some cases and the locality requirement does not apply to the states either) under the 6th Amendment. Only a couple of states choose to allow non-unanimous juries, however.
The right to be indicted by a grand jury prior to being prosecuted in cases charging an "infamous crime" (i.e. a felony) under the 5th Amendment. About half of U.S. states, mostly in the Eastern U.S. retain this right.
The right to a jury in a civil case under the 7th Amendment. In practice, the vast majority of the states honor this right as a matter of policy, however.
The prohibition of excessive fines under the 8th Amendment. Many states have comparable prohibitions under state constitutions, however.
There is not binding case law in all parts of the United States on the incorporation of the 3rd Amendment on quartering soldiers under the 3rd Amendment (but this is not a big deal since there are very few soldiers who don't count as federal who seek to be quartered in someone's house and there are other incorporated rights which overlap with this one like the 5th Amendment eminent domain rights that overlap with the protections of the 3rd Amendment, and because many state constitutions contains 3rd Amendment protections anyway).