My guess is that the map is being culled. I took a look on the Unity forums and see that other people are running into similar issues with Unity Tilemaps, which SuperTiled2Unity uses.
https://forum.unity.com/threads/tilemap-chunk-culling-bounds-confusion.537268/
https://forum.unity.com/threads/disappearing-chunks-on-tilemap.681136/
Try going to one of the Tilemap Renderer components on one of your layers in the map and play with the chunk culling values to see if that makes a difference. You want a culling size that large enough that it won't be culled out. If that "works" then perhaps you can add a custom importing script that will help set those values for you automatically.
In any case it sounds like a Unity bug. They won't be able to fix in time for your jam but when you have time it would be good to enter a bug with them. There's probably something special about objects that are part of a canvas that is failing to automatically update the bounding chunks. What is your runtime target? It could be a bug there too.