They got the math generally correct enough to match observations (although not really, gravity fails in a lot of things like explaining the motion of the galaxies, and needs the universe to be filled with dark matter/energy to work). The main problem is that of scale. The stars and celestial bodies in RET are much bigger than the ones in FET, which shrinks the power of 'gravity', and somewhat changes its nature and implications, under the FET model.
Also, it is possible to accelerate indefinitely in space. This concept is not even cherry picking Special Relativity Theory. The relativity of motion was spoken about in Ancient Greece by Aristotle and others after him. It's old! The only new thing Einstein brought into his rip-off work was lumping it together with the relativity of time.
For a body traveling at 9.8 meters per second per second, from one second to the next it has increased its acceleration by 9.8 meters and has traveled that distance. It does not know about, or is affected by, or cares about, the previous increases in acceleration. In its reference frame it is static from one moment to the next. At some observation point, perhaps, 9.8 m/s/s would be appear to approach (but never quite appear to reach) the speed of light. The keyword is: appear.
Speed is relative. It is an outside observer phenomenon. An asteroid in space can be traveling 4 miles an hour or 4000 miles an hour depending on the speed of who is looking at it, relative to that asteroid.