Move damn you!

Ok... so how do I bring players and their characters with me when I swap maps?

You don’t. You should Copy the tokens and Paste them to the new Map.  Unless you have a Pro subscription and an API script to handle this for you. But I suspect that would cause more problems than it solves. I’ve always used Copy & Paste. 

There is a "Ribbon" on the page listing; drag-and-drop that to the new map to move the players. Either you should already have placed PC tokens there, or you can place them now (copy and paste from the previous map, or drag-and-drop from the journal). 

I would add that I was getting problems with UDL and token sight a while back.  It turned out to be that I wasn't cleaning up behind me and thus there were multiple copies of the character tokens across several maps and this is what broke it.  Reducing the number of tokens WITH SIGHT (inc NPCs) to 15 or less fixed it.  This may have been OBE now, but something to flag in case you get a snag :)

Mark G. said: There is a "Ribbon" on the page listing; drag-and-drop that to the new map to move the players. Either you should already have placed PC tokens there, or you can place them now (copy and paste from the previous map, or drag-and-drop from the journal).  Oh my goodness thank you.