"But, radio waves can't travel through metal", I hear you say.
Nobody says that. Why would they? Sure, conductive materials attenuate signal, and metals are typically very conductive, but real-world metal structures, often made of metals and alloys not optimized for high conductivity, are in fact plenty "RF transparent".
We do make simplifications like "a metal surface is a good reflector for RF", but it's not hard to keep in mind that it's only a good reflector, not a perfect one, and that it's a simplification.
Well, you know that, and I know that,
Well, I know it's wrong!
If I use the best antenna (say those dish antenna thingies)
A dish is just the reflector, not the antenna.
against a thin sheet of metal,
Thin, as well-known, means "lets through RF energy"; you'll want to read up on "skin depth".
It's really not a surprising concept if you know the physics: Maxwell's equations in materials simply allow for propagation of wave in anything but superconductive materials – and if your material is thin enough, yep, the wave will "travel through it" (the usual ray physics of partial reflection, diffraction and refraction still apply).
use a extremely high wattage (say 100,000,000 watts)
Why? Attenuation is something that happens as proportionality of output to input. So, instead of inserting 10⁵ W to get, say, 1 W out, insert 0.1 W in, and still get 1 µW out: that's very powerful for a radio receiver.
I know it sounds silly
Not at all. It just means you have a lot of things to learn about how RF waves actually work! So far you seem to be going from over-simplifications, and since you actually seem to care deeply about the matter, your only way forward here is to learn about the physics actually work.
Your approach of inserting high powers, thinking a dish is what makes for a good antenna, and the misconception that EM waves don't travel through metal suggest to me that you've been learning from bad educational material, and now you notice that what you've learned doesn't work in reality.
So, get better material to learn from! We don't know your background, so I don't think we can advise extremely well here, but:
You've got a general license; so, resistors, inductors and in general impedances do not scare you! So, maybe the ham-friendly style of Nahin's The Science of Radio (buy it used, maybe?) might be the right thing for you? It's a book that doesn't assume too much math (basically, just a bit of calculus), and goes into the topic from a radio operator's point of view, through historical steps.
Advertisement for "National Radio Institute Education", from Nahin's book, where he used such ads lifted from 1970's fiction pulp magazines to brighten up the book's flow