Yes, this thread is about the code rather than the common law, so that's what I'm focusing on. If there were a simple repeatable common-law remedy for the "wage slave" as opposed to the sovereign who can easily withdraw, given the problems they face, I'd focus on that too.

couldn’t I just hold the agent liable

They deflect everything you give their agents as personal attachments. If you are willing to email your workplace, you should be willing to testify to the IRS to the facts you know before it goes a lot farther.

I simply ask for a bill of particulars

Good, but what happens when the IRS contacts your workplace or bank with a lien or levy? Suddenly you're older Joe Lewis with tons of power but no liquidity. He wasn't the only one to wake up with his cash zeroed like a terrorist, and my allusion is hiding a whole world of destruction of lives. The purpose of early testimony is that it protects you before it goes that far.

But I can claim it, it’s just why would I want to unless I’m burning bridges.

Your workplace knows nothing about how much you claim out of your withholding after they've completed their middleman work in January each year. There are no bridges burned with the workplace by making a proper claim with the IRS.

I don’t think one should be filed at all but because I had previous withholding, it would be necessary. A w-2 is used to confess “income” to an “employee”.

Good, and now we're coming to the meat. Remember that "wages" are different for the two purposes, Fed WH and SS/Med. Nature of "employee" is also different for the two.

I can’t be an “employee” because my company is not “engaged in the performance of the functions of a public office”.

That would only work if you were being asked about the definition you quote, "trade or business", which only comes up for the self-employed. You could still be an "employee" under either or both of the two other definitions. We're constantly dealing with scoping, words that change meaning based on context, to an extreme degree.

3401 failed to define me as an “employee” so none of their definitions of “wages” apply to me.

There's your first hump. None of the chapter 24 definitions by this standard (we'll get to the chapter 21 definitions). For Fed WH purposes (box 1), you have legally determined that you are not a 3401(c) "employee". A person who has made that determination can truthfully testify on form 4852 attached to 1040 that they have made attempts to contact the workplace about the error (copying your letter), that the error remains uncorrected and should be corrected to the amount specified, and that they have determined themselves not to be a 3401(c) "employee". (By the 1940s, when withholding at the source was piggybacked onto Social Security to produce more taxpayers, the lawmakers realized that the ambiguity of the word "includes" was not being contested by anyone and they could set up "volunteers" in plain sight, especially with the war and Donald Duck and all. Earlier they had to be cagier.)

For 3121, (d)(2) is a bit confusing.

Indeed, because in the early 1930s only business owners were paying personal income tax, so when SS withholding was invented and sold as a savings plan rather than a tax it had to rely on the cagier definitional track. So let's assume for the moment that a 3121(d) "employee" (SS/Med) is not the same as a 3401(c) "employee" (Fed WH), and that a 3121(d) SS/Med employee is (and includes) just the ordinary meaning of the word, a common-law employee. Did SS law fail to create an excise nexus, thus running the risk of unconstitutionality due to impinging the constitutional right to exchange labor for money? No, we just look further for the nexus. I've discovered that there's always a nexus. Go back to 3121(a), which talks about the withholding to be paid:

For purposes of this chapter, the term “wages” means all remuneration for employment, including the cash value of all remuneration (including benefits) paid in any medium other than cash; except ....

Nothing about an "employee" in that sentence! Just "employment". Employment is the nexus for SS/Med, but employee is the nexus for Fed WH. Now reread my earlier note about 3401 vs. 3121. (I may have mentioned 7701 too hastily as global definitions for the whole IRC, because there's a backup definition in 3121 also useful that doesn't conflict, and either route works.) Getting over the second and final hump won't take "a lot more time" with that much help, and I think you're willing to see it, and it covers 3, 5, 7 all together. And that is all the pieces you need even if my account should go silent.

("Compensation" has multiple meanings, and I thought there was a quick demonstrable route to show which one is intended for W-2 but I'm not finding that immediately. The reason it's less important is that it's generally a catchall term for things that are not cash-for-labor, such as investment benefits. Unless you have an adjustment to these boxes that causes their totals to differ from your final pay stub gross total before withholding, there's no compensation to worry about, just earnings.)