Yes, it has been fairly civil, although the base premise is seriously flawed right out the gate.

Energy is defined as the capacity of a physical system to do work. Energy is transferred from one form to another, i.e. potential, kinetic, light, thermal(heat), mechanical, etc. Energy IS NOT transferred from one body to another. This is where the Law of Conservation of MOMENTUM comes into play. And yes, the ballistic pendulum has EVERYTHING to do with it. In your example, the hammer is considered a physical system, which at rest under the sear has its energy as potential. The spring is an external force which acts on the hammer once the sear is released. The hammer's potential energy is transferred to mechanical and kinetic energy for the duration of the angular travel around the hammer pin. Once the hammer strikes the firing pin or primer, momentum is transferred to the the object being struck and once again, the hammer's energy is potential. Now, the mass of most firearms is significantly greater than the hammer, so the velocity component is negligible; and frankly is quite rapidly overcome by the thrust of the weapon rearwards in response of the gas and projectile exiting the muzzle. I'm trying to keep this as simple as possible, but the spring is also considered a physical system.

The point of contention as you put it Rod, is when the projectile arrives at the intended target. The kinetic energy of the projectile, which is usually increased to promote sales of newer and "better" cartridges, is transferred to various other FORMS OF ENERGY, such as the above mentioned heat, sound, and potential if the projectile does come to rest in the body of the game. The MOMENTUM of the projectile is transferred to the game; again most game animals are significantly greater in mass than the projectiles used to bring them to bag. Therefore, the velocity after the collision does not tend to "move" them. Over-matching bullets for game animals rarely occurs, but makes for some spectacular kills on varmints. One case in point was when I applied about 1,700 ft-lbs of kinetic energy (a calculated number) to a cow elk with a 400 grain Speer Gold Dot from my .475 Linebaugh. The bullet broke the left femur and was recovered under the hide of the right shoulder. If there was a shred of truth (which there is not) of energy transfer between bodies; I hit that girl with about three horsepower. One unit of horsepower is equal to the power needed to lift 550 pounds one foot in one second. I should have moved that 500 pound cow at least three feet by increasing her potential energy by converting it from kinetic energy. Your wooden block analogy is misunderstood in that the mass of the blocks is not proportionately large enough to negated the velocity following the collision. Although they do move, the relative velocity is much slower. Setting the post in the ground allows transfer of momentum to the ground which as everyone should know by now has the mass necessary to negate the after collision velocity.

Now regarding the cast versus jacketed bullet discussion. Yes, one needs to match the bullet to the game and cast bullets are wonderful if used properly. Show me someone who complains about smoke and leading and I will show you someone who has most likely not taken the time or doesn't know how to properly use cast bullets. I think both types have their place and use them as I see fit. However, any situation I need penetration, the cast (solid) is going to win out over jacketed. Large flat meplats create tremendous wound channels for their size; but that is a topic for another thread.