The last article “What’s the Difference between Qualified and Non-Qualified Annuities ?” does not apply in the matter under discussion–although timing may have an impact. (Timing is another discussion so I will restrict my remarks to the difference between a deferred annuity and an immediate annuity. For example, in most Tax LLM programs, Timing is a separate course.)
The author discusses qualified & non-qualified annuities that are deferred annuities, but fails to address immediate annuities. In the instant matter, no deferred annuity is involved.
Perhaps if the author had taken the time to earn a CFP, CFA, or CPA professional designation, he would not have made such a glaring error.
P.S. In the situation under discussion, taxation gets more complicated than in the instance of a deferred annuity whether qualified or not. And, yes, I do understand that taxation is an ancillary issue not germane to OP’s concern. I made this note regarding taxation because the author of the article you cited discusses taxation–none of which applies in this situation (although, once again, timing can be an issue).