Hi Bret,
This sounds like two separate issues. The difference in publishing with Survey123Connect vs. the website should not affect the ability to migrate the survey. During the migration script, are there any messages that appear that might indicate something is amiss? Another common error I found during development was not specifying the correct timezone- in North/South American contexts, it can lead to no rows copying over as the records are from the 'future' (time in UTC vs. local time) and thus after the synchronization time.
On the other view/non-view part, with the December release of Survey123, the website now takes advantage of a new feature in ArcGIS Online - the ability to create 'Feature Service Views'.