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Well, in regard to your fourth "method" of becoming biologically immortal, I read something a while ago about some scientists that effectively stopped aging in mice livers. Basically, as people (and mice, apparently) become older, their cells become less efficient in many ways, including the cleaning up of sometimes damaged protein. This can lead to the buildup of toxic materials in these cells; this buildup is especially pronounced in diseases whose symptoms are mostly acquired in old age, such as Alzheimer's, Parkinson's, and more.
These scientists also found that more protein clearance helps prevent some of the "old-age" declines in function in mice.
Thus, if findings show that there are ways to enhance protein cleanup in humans using specific drugs or other methods, we may be able to use this same cleaning process in human livers and other organs and may well stave off the process of aging for a little while.
There are other options that I've read about, some involving stem cells, telomere shortening as mentioned above, and more.
With all these exciting advances, biological immortality may be achievable in the next few generations. The real question is, do we want it?