Much appreciated.
What I’m understanding from all that is that
the Einstein thing about mass approaching the speed of light is wrong and does NOT likewise approach infinite mass.
No, he was right. The fact that the mass of the proton mas increases by a factor of 7,500 is fairly amazing. If a 100 pound weakling made the same speed, he (or she) would weigh 375 tons. Granted, that's not "infinite," but it's also not going the speed of light in a vacuum.
The fact that the mass increases is why it takes so much energy to impart more speed, once one gets to relativistic velocities. At this velocity, slight increases in velocity create significant increases in mass.
Said another way, the "TeV" limit results in a mass (and corresponding speed) limit. It would take infinite energy to obtain infinite mass.