Well I chant the current LOTH daily, and in Latin.
I’m guessing you can chant it just fine. My pre-conciliar Monastic Breviary does not have any specific rubrics for this. I suspect generally you will find rubrics for private recitation, and singing the Office in choir. But no restrictions on chanting in private. What matters is that you use the correct texts. You can chant recto-tono (which is really just reciting), in-directum with recto-tono antiphon, or with antiphon and psalmody according to the correct mode, but for that you will need an approved antiphonary; from which the hymns should also be taken. There’s much less wiggle-room in the EF Office. In the OF, for example, for hymns you can substitute a simpler melody of the same meter if the given melody is beyond your skill range. I cannot say if this is the case in the EF.
Someone more familiar with the EF Office will probably be able to say more. But I would say, with my more latin legal mind, “if it is not prohibited, it is permissible”. A more germanic legal mind might say “if it isn’t permitted, it is prohibited”.
You might want to check out “Les Heures Grégoriennes” for the OF Office. It has the proper decrees and concordat cum originali, and allows you to chant all the diurnal hours in Gregorian chant, with noted hymns, antiphons, responsories, gospel canticle antiphons for all seasons, etc. It isn’t cheap (around E200). For me it has the double advantage of having French (my mother tongue) alongside the Latin. It is in 3 volumes: Vol I is Ordinary Time, Advent and Christmas, Vol II is Lent and Easter season, Vol III is the sanctoral. You will always be in one book only, i.e. no book-swapping, everything needed for a given time or feast is found in the same book. Lots of ribbons too, easy to mark your places for those times you do need to move around. For Ordinary Time, the entire weekday Office is in one place; on Sundays you move to the Proper of the Season for the gospel canticle antiphon and collect.
Honestly, I just finished a few days in the Monastic Office for giggles, it’s about the same length (150 psalms per week) as the EF breviary. Between the length and the book-juggling, it’s a relief to be back into Les Heures Grégoriennes. For the Office of Readings, I use Liturgia Horarum in Latin, either recto-tono, or using my own self-concocted Nocturnale built up from Ordo Cantus Officii references.
To me liturgy should be a thing of beauty. That means it must flow smoothly, have times of silence to contemplate what was just read/sung, be chanted slowly, correctly and deliberately, and practiced faithfully (you get better at it with time). I find I can’t achieve that if I bite off more than I can chew (hint: I am an oblate, not a monk). When rushed or very tired, simply recite the Office quietly.
That is my free advice. As I say to my kids, my advice is free, and you get what you paid for
