So in the end I had put the cake in the oven mostly unsliced. The next day I pulled it out and sliced it all up. The layers were still separating, probably because the cake as a whole didn't heat up enough.
I then put the cut up slices back into the oven at 170 for 2-3 hours again. This time the layers seem to be better stuck.
I think that the cake layers will darken more. But we shall see.
These are really large slices! They are each over 6 oz.