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I'm not claiming that the magnitude of the spacetime interval is not
invariant.
I think I can show that the spacetime interval ... is not invariant ...
I'm claiming that, since the assigned positions of E1 in F
and F' don't coincide in space (meaning they are not independent of any
reference frame), at times later than t = 0, lines drawn between E1 and
E2 representing the spacetime interval between E1 and E2 in F and F'
don't coincide in spacetime (meaning they are not independent of any
reference frame). In other words, they aren't the same line.