First of all, I would start off presenting yourself: Dear XYZ support team I am the web developer in charge of example.com website. By presenting you this way, you are establishing the frame to treat you, hinting that you should be presupposed to be somewhat proficient, so they could choose to answer in a more technical detail.

Feel free to hint, brag, or both! The best CS reps should easily take a hint from clear language and a signature like John Appleseed, JavaScript/Ruby Developer, but any will catch on with a simple line like "I know what I'm doing, so I'd appreciate an extra-technical explanation!"

Hey, I'm a PhD in [field] and do [whatever] professionally. Before calling you, I've narrowed down the problem to [something on their end], so that's what needs to be addressed. If I could speak to an engineer about [specific problem], that'd be great; but if we've gotta walk through the script, let's just knock it out quickly. If they end up requiring the script, then the best way to use your expertise is to run through it quickly. Keep the chit-chat to a minimum and just do the stuff efficiently. If they start describing how to perform some step, you might interrupt them with, "Got it, just a sec.", then let them know once you're ready for the next step.

However, what speaks against just straight up telling them that you're working as [Insert title of your position] and you know what you're talking about?

OP is referring to letting people know they can speak like proper adults when talking about technical terms, without going through the usual nanny-like discourse that tech support has to provide to non-techies. For instance, it happened to me with Amazon support. The speaker told me exactly where to touch in order to clear the cache of the Android Amazon App Store. Given that I work as an app developer the guy could have just said "please clear the cache". No need to go through "tap here, then here, now you should see this, tap that"...

I have tried different tactics of showing the tech support that I am proficient in their field of work (I work as a web developer). Specifically: using accurate terms and technologies to show my knowledge of them and telling the support that I am the "administrator" of the website in question.

How to let tech support subtly know that I am proficient without showing off?

Can't upvote this enough. It is highly irritating to see language destroyed (and we wonder why kids bastardize the language..).

there's no reasonable way to communicate effectively with the less technically minded without acquiescing to the nontechnical misuse of the term "hacker"

The more easily relabeled of the two uses of the term "hacker" is the malicious security cracker: it is not only the more recent phenomenon to acquire that label, but also the one whose meaning is most easily evoked by an alternative term. This is why, when you read an article of mine that talks about malicious security crackers, I use the term "malicious security cracker"

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(Vote: 7-2) Yes: The statute is unconstitutional because the constitution contains a right to an abortion.

Holding: The holding should directly respond to the question in the Issue Presented, begin with “yes” or “no,” and elaborate with “because…” from there. If the opinion says “We hold…” that’s the holding; some holdings aren’t so easy to pinpoint, though, so look for the lines in the opinion that answer your Issue Presented question.

The judgment below for that reason must be reversed.

Holding As the issue�s complement, the holding consists of two parts: (1) a “yes” or “no” conclusion to the brief�s issue and (2) the rule of law the court establishes. The rule of law is a guidepost that courts use to decide future cases based on the legal concept of stare decisis (judicial tendency to follow prior decisions).

the judge will state the legal issue(s) involved, her decision about the issue s (the holding) , and her reasoning.