Well, meabee you solve that problem by cloning/breeding those dogs. Let me explain.
The basic idea is this, whenever you find yourself in a level you can only complete by climbing all your characters on a stair, kill the dog. this may sound weird but, dogs in contrast to humans, can be easily breed/cloned.
So after you return to the bunker, a fresh dog will be available. so basicly, you can use dogs as cannon fodder (just like in the real world where a police dog is supposed secrifice himself when nessisary). This will offer some strategical intrest into them.
How to implement this, basicly by ading a fresh dog to the recruits list after your previous dog dies (killed by you or whatever)