Nice! It reminds me of Queneau's Cent mille milliards de poèmes, which has a good web implementation (link below).
One way you could put it on a static website would be to have a page for each line X containing the whole poem but starting with line X. A little JavaScript on the landing page will allow a random starting page. If they're all formatted the same then clicking to the next one would feel like scrolling.
https://bevrowe.info/Internet/Queneau/Queneau.html
