School of Prayer by John Brooks gives meditations and explanations of the Psalms. I think you would find it helpful, but it's a small book...I would look for a used copy.
Hey there! One of my parish priests will move his lips/whisper while praying the Liturgy of the Hours if he’s not praying it in common with other priests, as this was often (and still is in many seminaries) taught as the standard for praying the Breviary in private. Simply reading Lauds is still praying it, but maybe whispering/mouthing it can help.
A few years ago I started praying the Liturgy of the Hours as my main form of prayer each day as I found freestyle prayer and the Rosary weren’t fruitful for me at 6:15 AM or 9:45 PM when I had the time to pray. One of the main ways I reflect on the Hours is comparing the antiphon or the Scriptural heading at the beginning of each Psalm with the text of the Psalm, and comparing the Psalms with the reading for the day, finding different combinations. Often it’s just one little theme that may stand out, and because there’s a 4 week cycle I often find myself seeing the same meaning theme again and again. But this is ok! This is what God is trying to tell us to focus on at the moment, even if we can only focus on it for a few seconds, and as we grow in life and as we walk further along our spiritual journey with God, the same themes will always come back eventually. But this is nothing to be sad about - if we walk up a mountain by going around it, we will keeping coming to the same side of the mountain, yet we will be closer to the summit.
A great little book to develop praying the Liturgy of the Hours is The School of Prayer by John Brook. It’s technically written for beginners, but I only just recently read it and it’s helped me a lot, especially with the author’s commentary on the prayers of the 4 Week Cycle in the back.
As far as the hymn is concerned, you should still pray it since it’s integral to the Hours’ structure; but again, you can simply whisper/mouth it just as you do for the rest of the prayer. Soon the translations of the hymns of the Latin ordinary (hymns which originate from the first few centuries of the Church) will be published in the American and British LotH, so if the hymns right now feel a little too “sunshine and daisies” for your taste, you’ll be getting new options that are 100% theologically sound.
Lastly, persevere a little more in your current spiritual regimen. But if you find something lacking, then it’s ok to find a different way to pray.