@chinglu;
There are lots of "paradoxes" in relativity. Like this thread, people can and will go on and on about the interpretation of the paradoxes. Your particular paradox (inconsistency) seems to be very close to the "pole and barn" paradox first introduced into US relativity textbooks by 'Spacetime Physics', by Taylor and Wheeler (yes, John Wheelsr, a Nobel Laureate American Physicist). In there, you will find the answers to most of the objections you have raised here.
One thing you mentioned that I needed to think about was the "plane of simultaneity", which as far as I know, you have interpreted incorrectly. Points on such a plane outside of the "light cone" of Minkowski space-time physics, might be viewable from other locations (light cones) of other points, but is not viewable at all from within the SINGLE light cone related to a single event, at a single location, which is its vertex. Even points (pairs of other events) that are within the same light cone can be interpreted as simultaneous in one reference frame are not simultaneous in another, or an intersecting one associated with a reference frame that is moving with respect to whatever frame of reference that is chosen inside the first one.
@therestofyou Minkowski was a NINETEETH CENTURY college math professor. Please think about that for a moment and you will understand that while he had a fine array of classical mathematics at his disposal, he had almost nothing by way of physics on which to base his mathematically skewed conclusions. This is the 21st century. Each and every one of you who have complained about my own mid 20th century physics education (which took us to the moon, btw), have access to math, tools, and physics that were not available either to me or to Minkowski.
By endlessly chastising and berating someone like chinglu for failing to grasp the basics of relativity, and doing it with mostly 19th century math, well, it doesn't bode well for how far we have come, through the efforts of folks who are like you, to be sure. You have taught me not to engage in any discussion of Minkowski physics, and I wouldn't venture to do so again even if I had three PhDs in math, physics and relativity. If that's what you wanted, you won. Congratulations, 19th century mathematicians everywhere.
But don't stop with changlu. There's a guy named John Doan whose websites are still up and running on the internet after over 40 years. His particular obsession is with the twin paradox. He won't let it go, no matter how much he is chided about his lack of education and grasp of the simplest ideas of Special Relativity. Then there's David de Hilster's Autodynamics, who swears to be able to derive an equivalent version of relativity with only one observer or reference frame, and rails against any suggestion that neutrinos exist. Lots of crazies out there, but I'm just not all that certain that an obsession with 19th century mathematics is really very much better. That's all I have to say on the subject of this thread and any other having to do with Minkoski, whose name I will never mention again after the next sentence. Have a great Minkowsi rant.
You're going to be endlessly chastised for disrespecting physics and the folks who have done it successfully. So far you fit my delusional crank profile.