There might be more clever options, like cryopreserve everyone who dies; this does not consume many resources (the only recurring cost is liquid nitrogen, which is pretty cheap). Then we can wait to revive everyone until we have the medicine and the resources to support everyone, avoiding overpopulation.
Besides that, it is immaterial. We are all going to die someday and there is nothing we can do about it. The people seeing cryogenics are largely snake-oil salesmen. I don't believe anybody will ever find immortality (at least not in this life).
Do you think this problem is merely very difficult, or literally impossible to solve (e.g. because of some physical law)? I think that if a bunch of really smart humans tried really hard to solve this problem, and you predicted very very confidently that they would fail, then I would be pretty skeptical of your confidence. Just as an example, you suggest getting some more Earths. Sounds like one solid approach; expand humanity to other planets!
>We are all going to die someday and there is nothing we can do about it. [...] I don't believe anybody will ever find immortality (at least not in this life).
This might literally true, in the sense that we probably can't survive the heat death of the universe in however many bazillions of years. But do you think it is implausible that advanced medical technology could e.g. keep us alive, healthy, and sane for, say, thousands of years? This sounds both plausible and quite desirable to me, and I'm confused by your statements---for instance, I can't tell whether you are making a factual claim or an aesthetic claim.
>The people seeing cryogenics are largely snake-oil salesmen.
Eh? They seem pretty sincere; the people who run these organizations (Cryonics Institute, Alcor) are generally themselves signed up for cryonics, and speak passionately about life extension as a desirable goal. Cryonics is not exactly a get-rich-quick scheme.
Why? Do you think this would withstand a thousand years of human ingenuity? I'm confused where you're getting this very confident prediction.
It also still seems to me that long lifespans are extremely desirable, albeit difficult to obtain, and I'm not sure whether you agree. This is relevant because if we want to decide e.g. where to put research effort, it's useful to know what we want.
The article you linked is kind of long, and looks like it mainly consists of sneering at various people; could you point to the part that's relevant? All I saw was some stuff about Alcor messing up a preservation, which is pretty unfortunate, but not really strong evidence that they have bad motivations.
Also note that your current (probably?) western lifestyle puts several times more load on the environment than mine 3rd world-like one. It is the wasteful lifestyle choices made by living people that are really a problem, not the quantity of people in itself.