> In my view, we are just workers--our only leverage is our willingness to walk away, which is usually fine with the company. They have a long line of candidates out the door.
You have more leverage than that; not all workers are equal. That's why interviews exist in the first place. Maybe you have prior industry experience, or experience with some paradigm/framework they want to adopt. Feeling like that probably hinders you in negotiations; if you're arguing that workers are largely interchangeable, it begs the question why they would hire anyone other than the cheapest possible person.
On your decision tree, you're missing a step where you explain why you're asking for more pay. The most compelling argument there is frequently a competing offer from another company for more money (which is evidence that what they consider "market value" for you is too low). Other than that, you can argue that they're misjudging your value to their company. Your industry experience should add value, or your ability to be a leader among ICs, etc. You'll have to justify why you should be paid more.
You've also entirely left out negotiating. If you're not happy with response 3a or 3b, propose an alternative. There are several compensation alternatives to salary.
In terms of pure cash, you can ask for a sign on bonus. Those are typically paid out of a different pool than salaries, and can be easier to negotiate than a salary increase. It's also CAPEX instead of OPEX, which I believe is preferable to a business (just based on what companies have told me, I don't know the entire reason why other than that it's a 1 time cost). If you have an idea of how long you'll be at the company, you can amortize the sign on bonus as part of your salary.
There's also a large array of non-cash compensations you can get. You can negotiate to work from home X days a week. You can negotiate for more vacation days per year. You can negotiate reduced hours for what they're paying. You can negotiate to have them send you to conferences, or to more than the standard number of conferences. You could probably have them give you hardware that's being decommissioned if that's your thing. Another atypical idea would be to have them pay for/subsidize/use their discount on an AWS/GCP homelab for you (that seems less likely to be possible because of issues with accounting, but can't hurt to ask). The limit is only your imagination.
I think aggressive is a misnomer here. I would call it assertive. You don't have to bang your fists, just know what you're worth to the company and maintain that you won't accept a lower value. If they say they'll pay X, you respond that it's below what you would expect for someone with your skills/experience/whatever and that the offer would be more compelling if it was $Y higher. What many people do is the opposite; they wait for the company to decide what they're worth and then they decide whether that valuation is acceptable to them.