So, is there any specific reason not to immediately Tame the Dogs? We decided on the first turn of the Dream that we can easily achieve it, by simply rotating the 1st tile (you don't really have a choice, it's literally the only thing you can do when you first spawn), moving onto the bones, and letting the dog move to our space at the end of the first turn, after which we can tame it at the start of the 2nd Turn.
This prevents future dogs from spawning (at least 2-3 of them from new tiles, plus however many Morph actions would occur). It also makes the Slumber card that gets added to the Slumber deck significantly easier to deal with.
It also made the scenario very easy, since basically all we had to do was walk around the map, use the levers, and spend green resources (Awareness or whatever it's called) until we find the exit, with no threat from enemies (ehrm, Entities, whatever) at all.