A discussion of 'Tachyons, the 4-momentum ...'

In DOI: 10.13189/ujpa.2023.170101, Figure 4 depicts a thought
experiment involving FTL communication.  This figure is
attached to this post.  We, the viewers, are at rest with
observers A and B.
At event E1, observer A, at x = 0, t = vL/c^2, sends an
infinitely-fast tachyon signal to observer B, who receives
it at x = L, t = vL/c^2.  B immediately passes it to D, who
is moving at velocity v.  D's clock reads t' = 0.
D is now going to send it to C.  The question is, where is
C?  Is C at x = 0 or is C at x = Lv^2/c^2?  According to
us (the viewers), C is at x = Lv^2/c^2, but if we (the
viewers) switched frames so we're at rest with C and D,
(see Figure 5 in DOI: 10.13189/ujpa.2023.170101).  Now,
it appears that D can send a signal to c at t' = t = 0
(infinitely-fast).
But according to our (the viewers) present position in
Figure 5, A (at t = 0) could only send the original signal
to B, who would receive it at t = vL/c^2, or the loop
would not be completed (because of the relativity of
simultaneity).
Let's move back to Figure 4.  So in order to complete
the loop, D must send the signal to where C is not (at
t = 0, x = 0), which flouts RoS.  But at t = vL/c^2, C
is not adjacent to A, so no closed loop can be completed
in this scenario.
Comments, Prok?