Makes sense - I actually realized the split screen would not do what I was hoping for anyway (which was to be able to right-click-drag to get a stamp from one file and use it on the other - it makes sense why this doesn't work).
Currently I'm working with layers and going from one to another to grab my stamps (set to the side of my main work area), but I think all I really need to do is have my tiles area of the canvas copied to all layers.
Unrelated - I noticed that undo-redo sometimes doesn't work with color changes or outline tool changes (can't remember which). I also think to NOT shade the work area when the tool window is open would be a good change (because when you preview changes the shading makes it hard to see accurately).