I'd love to see something written up about how quickly this converges, assuming the variables are i.i.d and distributed according to the distribution in the article.
Empirically, from running a quick script on the data in the article, it seems like you only need to sample 5 numbers to get a distribution that looks uniform using this "sum mod 10" method.
If you're going for empirical, why not ask for between 1 and a very large number? May as well extract as much entropy per person as possible for post-processing.
Mod10, no matter how large the number you’re only keeping the last digit (assuming they choose base 10 numbers), which... is probably no more random than asking them for a single digit in the first place.