So I started with a brick. I thought of making a little fabric bag for it, but then I had an even faster solution: a basket I already had on hand.
Ta-da! The basket keeps the brick enclosed and not crumbling anywhere or scraping toes or walls. The basket handle makes it easy to grab and move. When the doorstop is no longer needed this winter, the brick can go back to the garden and the basket can go back to the cupboard. Truly, this simple solution just makes me so pleased.