How is it possible for psychometricians to develop IQ tests for people smarter than them? After all, while psychometricians definitely have above-average IQs, they probably don't have IQs over, say, 160.

If psychometricians already know what the right answers are (and how to obtain the right answer), then wouldn't they score very high on the tests, even if they're not THAT smart? (making it possible for other people to score high on the tests if they studied psychometrics as well?) The format of the test isn't going to vary that much from administration to administration. Of course, the tests are timed, but it's entirely possible that the practice the psychometricians get from writing the tests could easily make them better at each of the subsets of an IQ test.
Short answer: 
construct a usable chair out of toothpicks. Now, I certainly can't do this, but I can verify your answer easily enough

Long answer:
Verification of answers is often a lot easier than producing answers. And thats not just anecdotal, there are computational and psychological reasons behind this fact.

Computationally - complexity is different for solving a problem than for verifying it. For example the clad of NP problem cant (probably) be solved in poly time, but they can be verified in poly time.

Psychologically - think recall versus recognition. Recognition just involves your brain lighting up when it sees the right answer, whilst recall or production requires an extensive search at the very least

So the answer is that the test makers don't have produce the answers themselves, and certainly not under test conditions. They simply have to be able to see that the right answer is right (either produced via a group, a computer, or a genius).

Also, remember that no one question separates high IQs from low. Perhaps a 140IQ could answer one of the hardest questions, but not all of them.

Lastly, remember than IQ isn't a single dimension, perhaps the test was written by one expert in each dimension, which could then identify a genius in all dimensions