It' just a conversion factor here, like the one to convert from inches to centimeters.
2.54 cm/inch is dimensionless because cm and inches are different units in the same dimension. If m2/s2 is just a conversion too then length and time are just different units for the same dimension. Time would literally be a 4th spatial dimension, and every length in space would be time. Not can be converted to time, but is time. Is this what you're saying?
E=mc2 converts from kg to joules. True, the units aren't in the same class (energy and mass), unlike my example with inches to centimeters. But it's still just a conversion of sorts. It would be like converting from mass to volume for a given substance, e.g. 1kg of water at ~40C is 1 liter.
So when Einstein says that mass and energy are the same, is he saying that length and time are the same? It's like Einstein has mass = energy and length = time and now you present mass = volume. It's interesting that volume is length3, so your univers must be a co-universe to Einstein's, where mass = length and energy = time and the density of water is a universal constant.
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