Sorry, I've noticed my mistake. We are working in units where the speed of light is given the value . This makes time measured in metres. One metre of time is defined as the amount of time it takes light to travel one metre of distance. With this, the Lorentz transformation is

If we were working in SI units, where , then we use the other transformations we were trying before AND the spacetime interval is

So to solve your problem of , not , use the set of equations above where . Sorry for the earlier confusion.