Just passing by, reading a few posts here and there. Here are a few
comments to the quoted.

* * * * Example 1 (contrary example)

* * * * I observe a pendulum clock coming straight at me. SNIP.... Goodbye time dilation!

Pendulum clocks do not operate in inertial frames (devoid of grav.
field). Pendulum clocks work on earth because of the grav. field and
this the surface of the earth is non-inertial hence SR does not
apply, does not conclude.


* * * * Example 2 (proper analysis)

* * * * Let's say I have 2 identical synchronized clocks initially together in the same FofR.

* * * * I now apply a bit of a force to one for a little while so I have now introduced a bit of a relative v between them.
Let's say I let this go on for a million years or so and then apply the moderate forces necessary to get the clocks
back together in the same FofR. So overwhelmingly, both clocks have been in different inertial FofR for a long time
with a relative v and the force and resultant acceleration can be entirely regarded as insignificant

Insignificant? Do the math. There will be a non-zero "de-synch" as
predicted by SR(+clock hypothesis) and as observed by actual
experiments.


Most people think that time dilation
means that time is actually passing at different rates

Yes, some people *interpret* it like that.

Relativity itself
states that this is "apparent", not actual.

No, Relativity does not state that. Some people state/call/interpret
it like that. Relativity simply gives you its predicted
VALUE(s); it gives you the values on the clocks and is independent of
how you call this.


* * * * The stupid part about this is that the theory itself claims that time only "appears" to elapse more slowly,


Again, NO, the theory ( Relativity) does not make such claims. Some
authors simply *describe* it that way. 10 20 no matter if you call
this real, apparent, slow, fast, different rate etc.