In my graduate education, the idea of mass dilation was deprecated. It is after all predicated on the imperative to preserve F = ma. It was pointed out that mass became a directional quantity, since the particle's resistance to perpendicular acceleration was not increased at all, so it was better to identify the concept of mass with the "rest mass", and simply adopt the relativistic momentum, presevering the Newtonian F = dP/dt.
I arrived at the idea that "hitting power" was the measure of speed to be adopted, instead of travel time, much as in ballistics. A bullet going at 0.99c is going to dump 7.1 times its rest energy into a target, compared with 2.3 for a .9c bullet, so it has about 3 times the kinetic energy even if it's only going 10% faster by elapsed time.
It's interesting. I've seen both tennis and hockey commentators speak of "heavy" shots, as though there were some mystical ability to impart momentum to a ball or puck, independently of making it go faster. Pffffffthathinatin'