When I worked for Penguin USA and G.P. Putnam's Sons - I worked in Academic Marketing & Sales and Special Sales, respectively. Big 5 Trade book publishing houses don't just have A Marketing department, they have several marketing and sales department for children's books, Young Authors, Back List etc... Here's where I'l will post some ideas on ways to distribute your titles beyond bookstores and online retailers such as Amazon. If you think of some please include them too.. Thanks to @Sharon Wilson for reaching out and remind me!
For starters:
How about writing a grant for your favorite charity that could benefit from your book? This way your charity can purchase your book wholesale and distribute it to the stakeholders. Not only is your book bought, it's also distributed it too!