The minhag among some chassidim, including some very important Rebbes, is to daven very late, even past the zman tefilah. The Kozhiglover (Eretz Tzvi I:36) takes note of the criticism of the misnagdim and does his best to mount a defense. Let me just say that if you are a misnaged, I don't think you will be convinced, but that doesn't mean you can't enjoy the beautiful creative torah of the Kozhiglover. After working out that davening after the proper zman counts as a nedava and is not a bracha levatala, the Kozhiglover addresses himself to the question of how these tzadikim can put themselves in this situation where their tefilah counts only as a nedava instead of davening earlier when their tefilah would count as a fulfillment of the ikar chiyuv. Isn't this at best a b'dieved? One of the ideas he suggests is based on a Tosfos (Brachos 14) that discusses whether one should says a bracha on a minhag. Tosfos quotes that Rabeinu Tam distinguished between the minhag of tiltul aravah on hoshana rabbah, upon which no bracha is recited, and the minhag of reading hallel on rosh chodesh, upon which a bracha is recited. The former he calls, "tiltul b'almah," as opposed to the latter, which is a mitzvah, akin to all the mitzvos we recite a bracha over on Yom Tov sheni in galus, which is only a minhag. That's all Tosfos says as far as I can see, but the Kozhiglover "quotes" or explains the distinction as follows: we never recite a bracha over an aravah, but we already recite a bracha on the mitzvah of reading pesukim -- the bracha of talmud Torah. Given that a bracha can be recited over pesukim in another context, the bracha of hallel can also be recited. He then asks a question on this sevara (which again, does not seem to be a direct quote of Tosfos to begin with) -- how can Tosfos use apples to prove oranges? How does the fact that you can recite a birchas haTorah before reading pesukim of hallel prove anything with regards to reciting a completely different bracha of "likro hallel" over them?
Had you asked me, I would have explained the distinction as follows: the minhag of tiltul aravah is a fabrication from nothing; it is a new halachic entity which has no existance outside the context of the minhag which created it. Therefore, it does not warrant a bracha. Reading pesukim, however, has significance outside the context of hallel, just like the mitzvos done on Yom Tov sheni have significance outside the context of that particular day. The minhag of reading hallel or observing Yom Tov sheni took an already existing halachic construct -- reading pesukim, doing certain mitzvos -- and simply transferred it to a different time or a differnet context. Therefore, a bracha in these cases is warranted.
The Kozhiglover's explanation is structured not that different from mine, but it ventures off into what he admits is "derech aggadah." He explains that whenever a mitzvah is done, it flies up to heaven and transcends the boundaries of time and space that exist in this world. Tiltul aravah has no inherent mitzvah-meaning, and therefore it can never make it up to those transcedent heights. The words of hallel, however, are words of Torah -- we would recite birchas haTorah over them -- and therefore, they have the right "escape velocity" to break heavenward independent of the mitzvah of hallel. The Kozhiglover suggests a type of "migu" sevara: Since they have the necessary "escape velocity" to make it heavenward anyway, we can recite a bracha on hallel of rosh chodesh on these same words as well, because once upstairs, the limits of time and space no longer apply -- the distinction between days like rosh chodesh, ordinary weekdays, and Yamim Tovim has no meaning.
Based on this, the Kozhiglover answers his original question. Given that even a late tefilah can ascend heavenward based on its validity as a tefilas nedavah, and in heaven there are no boundaries of time and space, that tefilah has as much merit as a tefilah offered in the proper time period.
And for the icing on the cake, there is connection to daf yomi for you. The Mishna (Brachos 9b) writes that if one reads shema after the zman one has not lost anything; it counts as if the person was reading words of Torah. A footnote to the teshuvah of the Kozhiglover (not sure if it is his addition or someone else's) explains pshat in light of his chiddush: Since reading the parshiyos of shema count as talmud Torah, therefore the words constitute a cheftza shel mitzvah that can fly heavenward to a place where the boundaries of time and place no longer apply. In that special place outside the boundary of time, a shema recited before the zman and a shema recited after the zman count as one and the same.