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I don't know the science involved, so I'm hoping someone else does. But is it more probable a giant creature of that size and capability would be more likely to exist if it were, say, a silicon-based lifeform? Or maybe arsenic? I'm not sure what element would make the most sense on the periodic table, or if it doesn't make a difference. I'm just trying to find a potential way around stuff like, say, kaiju would probably be crushed under their own weight, their lungs would collapse, their metabolism would be out of control, etc.

We've had thousands of science-based questions where the square-cube law foils the author's intent. I could go on and on about that with a lot of prose, but these days I find comics more concise and educational.

Source: https://www.smbc-comics.com/comic/gojirasaurus

You are right that standard earthly lifeforms cannot grow to Kaiju size. In addition to your points, breathing and thermoregulation will be a problem.

Unfortunately, we do no know much about silicon-based lifeforms.
They might face the same scale problems.

One workaround might be based on the world of Pacific Rim movie, where Kaiju are created by advanced alien race, and sent in to wreck our cities. These Kaiju can be biomechanical creatures: most of its large body produced industrially and powered by some sort of fuel. But this body is 'piloted' by a living brain, getting info from biological senses, and issuing commands via nerves. The mechanic body will run out of fuel eventually, but Kaiju will be destroyed by humans even faster.