I bake sourdough rye (wholegrain Rye, salt, malt, mixed seeds and whole grains) and it's a very different beast to a wheat based bread, it does rise when proving, but it doesn't rise much in the oven.
It also has a tendancy to be sticky and wet in the middle which sounds like what you are having an issue with, I've found two reasons for this.
The first is letting it rise to long in the tin, if you let it rise more than about 1/3 of it's height it overrises in the oven and then collapses as it doesn't have the strength to support itself.
The second is the dough, it is a VERY dry dough it should
look like mortar.
Now rye isn't going to be exactly the same as what you are doing but since neither have gluten they may well behave pretty similarly. possibly not the best picture but I think you can see how dry the dough is in the bowl, the loaf in the tin on the left will rise to the top of the tin but that's all.