Specifically happened 2 missions in a row:
my assault in the first one used return fire with an Iconoclast (shotgun) and the game hung on their turn
my assault in t he second mission used overwatch with an iconoclast (shotgun) and the game hung on their turn
The commonality seems to be firing during their turn using a shotgun. When I swapped to an assault rifle the game did not hang so thankfully I was able to find a way to continue the game.