That doesn't solve the problem on Earth, it only spreads it across the solar system.
Immortality would change that but I expect by the time we figure actual immortality out we'll have either gotten off the planet or figured out brain uploads (this is what I imagine applying the reversal test to). In both those cases overpopulation is not a significant problem.
In the mid-term we're much more likely to see life extension and staving off dementia, and that would be helpful to countries struggling to sustain a workforce.
2) Brain uploads are dumb. Let me ask you this: I create a 'brain upload' program, run it on you, and tell you, "OK, now your brain is uploaded!" Will you walk willingly into a blender? You are your body. It does not matter what sort of digital derivative has been made of you, your subjective experience is tied to your corpse.
It's not harder, it's much easier. Hell, it's somewhat within our current technological capabilities. It's just expensive and we have zero economic incentive to do it.
No matter what our technological capabilities are at the time of doing so, I believe the first colonies on other planets will "suck" by the standards of living of that era.
The notion of the continuity of consciousness is not well-defined, so I don't think we have any idea about whether brain uploads can make sense or not. But I don't see why it's obvious that they wouldn't.
I agree with you about the brain uploads, but I think that the final conclusion is that either continuity of consciousness is an illusion, or it spans all life (i.e. pan-consciousness). Most cells, and all atoms, in your body will be cycled many times before you die. Why would there be any continuity of consciousness across those total changes? How is it fundamentally any different than the brain upload scenario?
The only reason why you think that your consciousness is continuous from even a moment ago is that you have memories of it (just like your uploaded self would, by the way). Just as you insist that you are the same person you were a minute ago, your uploaded self would insist it is the same person as it was before the upload.
1) My uploaded self would probably immediately be appalled at the loss of that subjective experience. You identify deeply with your embodied self; I am my vagus nerve and the intestinal distress it transmits as much as I am anything.
2) My embodied self would still have its own subjective experience and would experience dying, none the happier that there's some counterfeit digital version running around claiming to be me.
If it was well researched, well tested, had been known for some years to work, and I could meet with my virtual self and confirm his authenticity, then yes, absolutely I would. Assuming this "blender" of yours isn't painful, of course. What a small price to pay for immortality!
Consider taking a look at the book Glasshouse. It portrays a world where this is normal.