For those having the same issue I was, I found that my issue wasn't with the first 5 code cells that Zach had shared in an earlier post, but it was in how I was updating the form on AGOL. I was zipping the entire folder for the form in My Survey Designs after updating the CSV file.
In looking at Zach's code, I realized that he was downloading the survey folder from AGOL and updating the CSV from the downloaded form, zipping and updating that folder. The downloaded form has fewer files, so I realized that maybe some of the files in the original form's folder in My Survey Designs were allowing the Survey on the mobile app to update the CSV data, but not letting the web form to update the CSV data. As soon as I followed Zach's code and updated the CSV in the media folder of the downloaded survey folder, both the web form and mobile form updated.
Thanks Zach!