Dear CTR,
1) Reb Eliezer quoted correctly. It seems like you misunderstood him, because your explanation falls right into what he said.
2) Waking up late, is not the same discussion as davening late. For the sake of this topic, let’s assume that everyone rises before dawn, yet davens at different times.
3) Tefilla is a mitzvah at any point that the occasion arises. It is not specific to shacharis, mincha, and maariv. While it may be too late for shacris, it is never too late to daven.
4) Minaynim should be designated as times when the tzibbur will/is gathered. Using only halachic time considerations only, always seemed bizarre to me.
5) Every one of these minyanim is different than Reform, in that it centered on the Jew fulfilling his obligation, and not the requirements fulfilling the Jew. It is not comparable to the methods employed by the Conservative Movement, because there was no conscious decision to deviate. It followed a norm that preceded it. (See my post above.)