It's based on E=mc2. However, we can see it 'fall apart' when we set the value of c as 1

I don't think c is ever 1, except in very special units (light seconds per second?). It's 300000000 metres per second or about 670 million miles per hour. The equation that shows time going "backwards" is actually a bit more complicated, and my HTML isn't up to writing it out here clearly, but the clock slowdown factor is 1/sqrt( 1- (v^2/c^2)).

If v=c, then the divisor becomes zero, and 1/0 is infinity. If v is greater than c, you are taking the square root of a negative number: the result is an imaginary number and I can't think what imaginary time feels like. I certainly don't want it in my back yard.