The idea is a good one and could be true but the though experiment which was trying to disprove the energy has mass has a flaw and the rest of the argument is built on that proof.

The argument suggest that a mass with kinetic energy is accelerated by a force.
At some time later the kinetic energy is changed to mass and the author suggests that the mass of the body will increase. This is a faulty assumption. The mass formed from the kinetic energy will have the same mass as it did when it was kinetic energy.

The Equation E= MC^2 does not suggest that energy exists and has no mass properties.

Which has more mass a kilogram of photons or a kilogram of potatoes?

The idea that the radius R in the gravity equation changes due to contraction of space is a logical assumption and has an interesting impact on the relativity and gravitational force equations.

If you assume a yard stick shrinks in the direction of motion then as it accelerated towards an intense gravitational field it would shorten. Is the gravitational force now calculated using the shrunken yardstick to measure distance R or another coordinate system. If the shrinking yard stick is used then the distance ( in yards ) to the center of the gravitational field will increase as the yardstick shrinks. If this is accepted, then the question must be asked if there is a condition in which the yardstick is shrinking fast enough to make the distance to the center of the gravitational field stay the same or even increase?