I have my doubts about this analysis. Time dilation only occurs along the direction of motion. At the moment the two lances touch there is no time dilation component occurring due to evil George's horizontal motion so (as far as I can see) both lances have exactly the same vertical speed (but in opposite directions) and so exactly the same vertical momentum (but in opposite directions) due to the equal but opposite push that George respectively evil George give their lances. Another point is that the bounce off is depicted is from the "stationary" earthbound frame and not George's frame even though we are talking about how things look from George's frame. From George's frame the evil Georges lances comes in from an angle and will strike the top of Georges lance at an angle. George will first see his lance go up vertically (as he pushes it) but will after the collision be pushed down and in the direction of evil Georges motion. Finally from Georges reference frame his lance only has upward vertical momentum but evil George's has both a downward and horizontal vertical momentum. This may have no effect on the analysis but I think you would have to explicitly demonstrate that.

Unfortunately I can't modify my reply above. The paragraph starting with Another point.. is not correct.

I agree. I think relativistic mass has much the same status as Lorentz contraction. It can be a good way of calculating but it doesn't actually occur. In both cases we can explain completely through time dilation concepts. As you accelerate away from me you move faster and faster with respect to me. As a result I see your time dilating and so your acceleration diminishes: your see yourself continuing to accelerate with 1 m/s^2 for example but I see your second lasting much longer so the amount I see you accelerate in MY second is smaller. There is no need to introduce the concept of relativistic mass to explain this diminished acceleration at higher relative speeds.

The thing about the Atom in DC comics with Wonder Woman and Superman is he may be small but he can hit with his full weight, which contradicts how he can fall great distances such as ants do and be OK. Ant armour? For ant falls. Is there relativistic armour? What good would it be, except to fold away and hide in the bone marrow of Ironman.

The invariant mass sounds similar to clusters of galaxies with an isolated system of a gravitational lensing around it of dark matter. Invariant mass is measured from the seemingly center of all particles at a small scale, so if this can apply to galaxies, that is a grouping. Known factors = less bridging. This helps explain dark matter that prefers single, perhaps warmer galaxy habitation.