Is there such a thing as "genetic potential"?
Let me comment on what I see as the problem. And I won't use "genetic potential" since I'm a bit hazy as to what that means.
The house mouse is specialized for a particular niche. The beaver is specialized for a rather different niche.
Normally when we talk of mouse and beaver having a common ancestor, we assume that ancestor is relatively less specialized, and descendents just specialized in two or more different ways. It might be a lot more difficult for a house mouse to evolve in ways that causes it to lose its current specialization, then evolve a different specialization.
Going back to the Noah's flood scenario, with rapid evolution, the assumption could be that the rodents on the ark were relatively unspecialized, so could more rapidly evolve into a number of more specialized niches.
I don't expect it could possibly happen in the time available, and pink sasquatch probably doesn't either. However, the point remains that the evolution problem that needed to be solved might be significantly simpler than the one you used for comparison.