It seems that I am not the only person to suffer from the compulsion to versify psalms. Isaac Watts got there first some 300 years ago, as recounted in this article: Isaac Watts, Father of English Hymnody. An excerpt:
From an early age Isaac had a propensity to rhyming, and often even his conversation was in rhyme. His father became quite annoyed at this and told him to stop. When the rhyming persisted, the father started to whip the boy, and little Isaac cried out:
"O father, do some pity take
And I will no more verses make."