Say I fall into the event horizon of a black hole. As I cross the black hole, I would appear to outside onlookers to freeze in time, and would never move from that point again. In my perspective, time would seem to pass normally, so I would immediately fall into the black hole. But how? If an onlooker was to stay there and look at me frozen in time, I would stay frozen to them forever, even when the universe and time itself had ended. So my question is, how can I ever fall into the black hole if by any onlookers perspective I never do?
This is paradoxical but not contradictory because yours and the onlooker's times flow differently, and once you fall under the event horizon there is no way to reconnect to compare times. The paradox only happens because of the implicit intuition about some "absolute time" that applies to both observers, and that you continue to exist under the horizon "past" the end of the universe. In GR there is no physical choice for such absolute time, and in this situation one can not even make an arbitrary choice, spacetime does not split into a product of space and time. Krasnikov describes falling into a Schwarzschild’s black hole as predicted by GR in every detail, including perspectives of different observers.
"Another widely met statement is “From the point of view [or ‘in the reference system’, or ‘as measured by the clock’] of a remote observer it takes infinite time for a body to reach the horizon”... contrary to the first impression it is possible to give a meaning to that statement and even in three different ways... one of the three interpretations is simply wrong... Physically this means that all his — infinite — life α will be able to receive signals sent by his falling comrade before the latter reached the horizon."
But even the stronger "wrong" interpretation is achievable if you go deeper.
"In Reissner-Nordstrom and Kerr black holes under their event horizons (which are quite similar to Schwarzschild’s) there is another remarkable surface — the Cauchy horizon. And that horizon does have the property in discussion: an astronaut falling into the black hole reaches the Cauchy horizon in a finite proper time and crosses it in a point that contains in its causal past the whole “external universe”. Such an astronaut, indeed, will be able to see the death of stars and galaxies..."
How can I ever fall into the black hole if by any onlookers perspective I never do?
Because Oppenheimer's original frozen-star description is the one that's right. Have a read of The Formation and Growth of Black Holes on mathpages, where author Kevin Brown refers to two interpretations:
"Historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originially conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse. According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock asymptotically approaches "full stop" (i.e., running at a rate of zero). It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence. In contrast, according to the geometric interpretation, all clocks run at the same rate, measuring out real distances along worldlines in curved spacetime. This leads us to think that, rather than slowing down as it approaches the event horizon, the clock is following a shorter and shorter path to the future time coordinates. In fact, the path gets shorter at such a rate that it actually reaches the future infinity of Schwarzschild coordinate time in finite proper time."
These are two interpretations of GR. Most people only know about the second one, which involves future infinity and like Conifold said, "going past the end of time". I think it's wrong, and that the simple way to appreciate it is to ask this: has the infalling astronaut has crossed the horizon yet? The answer is no, and it's always no. He only crosses the event horizon in some mathematical never-never land beyond the end of time. In this real world, he never ever does.
Some people will challenge this and say it can't be right, because if it was right, a black hole could never form. But IMHO that doesn't pay enough attention to the "frozen" concept. The black hole can grow like a hailstone grows. If you're a water molecule alghting on a growing hailstone, you can't pass through the surface. But other water molecules can surround you and bury you. So whilst you can't pass through the surface, the surface can pass through you. Thus the hailstone grows. In similar vein the black hole grows, and you end up inside it.