After I while I found that this type of game can be frustrating as you are not incrementally solving the puzzle - instead there are multiple dead ends before stumbling upon the solution.
To make the site work as an 'app' you just need it to conform to the PWA (Progressive Web App) guidelines, and handle the install prompt. There's a good guide here:
Thanks. The 'share results' grid is about as minimal as I can make it without it being devoid of information!
The reset upon completion is intentional, as there is (usually) more than one solution to be found. For the purposes of stats recording, only the first successful attempt is registered.
The undo function is in the works.. to clear all you can refresh the page (or click the logo). There is an effect when a tile is filled but perhaps it needs to be more dramatic.