Actually, ZenBeam, that is exactly what Ring is doing. “Spacetime Physics”, by Taylor and Wheeler (the worst book on relativity I’ve ever seen, btw), uses relativistic mass throughout.
On p.232, the problem is to calculate the relativistic invariant quantity E[sup]2[/sup]-(pc)[sup]2[/sup] for different systems of photons and particles. They call this the “system mass”, probably as a way of making the invariance seem more natural.
I should be clear that the idea of relativistic mass is not wrong. It’s just different language. If you redefine the mass, then momentum is still p=mv, which some people find more natural. But a lot of physicists find it unnecessary – rest mass, energy and momentum are more than sufficient, and more natural, IMO, since a particle’s mass is not well-defined outside of its rest frame.