If relativity is symmetrical (triplets moving away and returning to the center) then what happens to the Doppler effect as seen by the moving triplets?
A B C
A should see C moving (Doppler) away/to faster than B C should see A moving (Doppler) away/to faster than B B should see A and C moving (Doppler) away/to at the same rate.
Note that the clocks (long term) in each case should match the Doppler (short term).
If I correctly understood your setup,
this spacetime diagram (on rotated graph paper to help visualize tickmarks along worldlines) encodes some observations,
which can be used analogously to determine all the other observations.
You can interpret the broadcast signals as birthday announcements. Then you can see how those announcements are received by various observers. You can see the Doppler effect for various piecewise sections of the worldlines.
(The diagram is taken from my answer to Triplets paradox and What if two twins flew off in opposite directions and were reunited in a perfectly symmetric way, would they have aged same? .)
