That broad caveat understood, I would like to give an update. I have found the experience of praying in this manner very beneficial, on several levels. Firstly, as I am an absolutely horrific creature of habit, I appreciate the ordered, rhythmic nature of structure of the Divine Office in general. There is enough variety day-by-day and hour-by-hour to keep my wandering mind focused, yet, the constant underlying structure and logic means that it's easy to jump right back in if I've missed a day or two (or, five... like I said, it's a work in progress). At this point, I have enough familiarity with the Psalms and Readings contained within that the subtle moods of each Hour have become more apparent as well.
All this is to say that I enjoy getting to know the various Psalms at what amounts to a more personal level. Most Hours contain just three Psalms apiece, so the effort of mentally digesting them is not Herculean by any stretch. The Hours that contain more than three Pslams (Sunday Lauds and Vespers, for instance) tend to have a more obvious thematic correlation, so they are more easily read as a group. In any event, the Psalms are the heart of the Divine Office, and it is both a challenge and a joy to pray them with the mind of the Church, considering how each might give voice to a petition, a sorrow, or a joy much wider than my own existence.
One last note is on the edition I have been using. It is a side-by-side Latin/English edition. Every couple of days, especially on Hours that have become more familiar, I attempt to pray only using the Latin. It has been a marvelous learning experience to commit a Psalm almost to memory in English and then consider the Latin version. Luckily, the English translation, from what I can tell, is quite literal. So, if I get stuck on a word, it is fairly easy for me to find my place. Not only is this helping my rudimentary Latin skills, it is also opening up a somewhat different mode of prayer than what I'm used to. Since I have what the Zen masters would call a "Beginner's Mind" about Latin, I am much more focused on considering the various words and phrases. This slows me down a bit and gets me to consider an inflected meaning that could be gleaned from the Latin version but not from the English.
If you may permit me a brief example (not that I can hear your protesting in vain!). The first antiphon for Monday Compline (Night Prayer):
English: Rescue me, Lord, because of Thy kindness
Latin: Salvum me fac, Domine, propter misericordiam tuam.
While the English conveys quite a beautiful sentiment, a deeper dimension is added when the Latin is considered. Rescue me conveys a sense of urgency - a dire longing to be free of our sins, perhaps. The Latin inflection of Salvum me fac completes the image by importing the language of salvation (salvum) more directly. We are asking for God to rescue us from sin by granting us His salvation. Are they the same meaning theologically? Perhaps, but there is, I maintain, a richness in the slight differences. Misericordiam also offers an interesting study. This particular word is quite common in the ecclesiastical lexicon, and is most commonly translated as mercy. Here, the translator has chosen kindness. Does this not beg a meditation on the relationship between God's mercy and God's kindness? If we break down the word Misericordiam we can see within it miser, which is approximately wretched, and cor, which is heart. So, God has a wretched (perhaps grieved?) heart for our salvation. Is this not His compassion? Is not His mercy moved by His compassion? Was it not His compassion and mercy that prompted Him to send His only Son to accomplish (fac) our salvation (salvum).
This is but one fairly in depth example, but there are (I'm sure) many more to be found. Translation is a delicate art, to be sure, as no one language directly equals another (as any multilingual person will tell you). In that regard, it is both intellectually and spiritually rewarding to occasionally veer down these translator's rabbit holes for the possible gain of an added insight.