HaShem demands multi-tasking from us, and this is actually one form of mesirat nefesh that is easy to overlook. There is a lot of cognitive dissonance in Judaism. There are numerous mitzwoth that we are commanded to perform all the time. Yet, we have a principle that when we are involved in one mitzwah, we are patur or free from the responsibility to perform another. Still, at the same time, there is a principle that we shouldn't pass over one mitzwah in favor of another. So how would we ever get from one all-of-the-time mitzwah, to the next? Not to mention when will we ever find time to do the mitzwoth that pertain only to a particular event or moment in time?
In truth, in the halachic framework, which is a truly perfect framework, I don't believe you will find any actual paradoxes. The structure doesn't violate itself. Yet to reach the level of understanding this perfection, and being able to perfectly navigate the sea of Torah at each and every moment is the intense work of a lifetime. If we don't work at it every day, we can be sure we won't get there.
In the cases mentioned above, mitzwoth of limited duration and pertaining to a particular moment in time take precedence over mitzwoth that are applicable all the time, to the best of my knowledge. Also, while we are patur from one mitzwah while involved in another, it doesn't mean we are forebidden to be involved in two mitzwoth simultaneously as is obviously possible when we say Shema Yisrael while wearing tefillin and tzitzith.
The point is not all of the fine detail in determining priorities in all of our mitzwoth throughout the day, that is literally the job of the halachah, instead I'm pointing out that it is a given that HaShem expects a Jew to multi-task. We can't pick one mitzwah and perform that to the exclusion of all the rest, we have to do them all, all 613.
This is not to say that we can't focus on particular mitzwoth, or that it is not important to focus on a mitzwah when we are involved in it, all I'm saying is that when Mosheh Rabbeinu told us לא בשמים היא - it is not in the heavens, one of the things he was telling us is that multi-tasking is possible.
Perhaps one important difference is that it might be that the human intellect is incapable of multi-tasking. However, when we bend our will to the performance of the mitzwoth and the service of HaShem, the nature of the world alters and makes room for what might otherwise be impossible.
A good example of this is what the Hesed L'Avraham (3:2) explains about the time of the Mishkan. When we left Egypt, the Shechinah wanted to dwell amongst us, but because of the great sins throughout many generations of mankind, the klippoth petitioned the high court of heaven claiming that the Shechinah should only be allowed to come down to dwell on Israel through the natural order, by first being clothed in the klippoth. This of course would mean that most of the blessing and divine outpouring would be siphoned off to the other side. Instead in this instance, because of the merit of the fathers of Israel, and their leaders, and because of the infinite mercies of HaShem, the Shechinah punctured a hole through the klippoth, defying the natural order, and dwelled with Israel until they arrived at the Holy Land, where the klippoth have no permission to enter.