I Googled around a bit yesterday and came up with a solution: using Google Sheets embedded on a page on our server:

http://media.herald-dispatch.com/elections2016/results.html

Refresh time is a mere few seconds, and multiple people can edit the document. AND it looks decent on mobile (at least, on the iPhone).

Forgive the colors, as it is a work in progress. Right now, it is displaying the same results in two columns to make sure I COULD put results in two columns.

I will have the different groups (state races, county races, city races) on different pages in the Google Sheets document.

I tried putting the code on a Blox static page, and on a section page, but I could not make it responsive. So, that is why I'm building it on our server.

These links helped me:

https://wp-glogin.com/2014/08/embedding-google-spreadsheets-with-more-control-over-appearance/

https://developers.google.com/web/fundamentals/getting-started/your-first-multi-screen-site/responsive?hl=en