Some excellent advice here. I recently wrote a guest blog on how to rhyme right in picture books on Tracey M. Cox's blog that might be of help.
For reading others who do it right, to Julia Donaldson, I would add anything by Mary Ann Hoberman and Linda Ashman.
Of my own rhyming books, I'm proud of On a Windy Night (325 words), a Halloween book, because it took me sooo long (8 years!) to get it right. I first wrote it in not-so-good rhyme, then rewrote it in prose with rhyming refrain at an editor's suggestion. Though I wanted it in rhyme, that made me figure out exactly how the story needed to go and the words I would choose to use. Then--after my own emotional experience of fear in dark and unfamiliar woods--I was able to rewrite it in very good rhyme and a rhythm that picks up speed. And the editor I sold it to spurred me on to make it perfect.
My newest picture book, What in the World? Numbers in Nature, was called an "elegant rhymed counting book" by the New York Times Book Review and "gracefully simple" by Kirkus. It took me 8 years as well. Word count was 150.
It is hard, but you're going about it the right way, Colleen.
Nancy Raines Day