HmH, you’re missing my point. If you’re carrying an electric charge but are not moving, there is no magnetic force acting on you. It doesn’t matter what other charges exist in the universe or how fast they are going: B x v = 0.
Now, your point about the True Frame is a little more complex and depends on which sect you belong to. The Lorentzians believe that there is but one True Frame, and to live in any other frame is to reject the divine. The problem, however, is that no one is really sure what that frame is, so naturally the sect has been rife with schisms and internal strife.
Seeing this, Electric God sent the Prophet Einstein who preached that there is no one Universal Frame, but rather that we must all be true to our own personal True Frame. Incidentally, that True Frame is the frame where we are at rest with the Divine. So, you need to calculate the Force of each particle in its own rest frame.
Then there are the Machians, who say that one’s True Frame is relative only to everything else, but no one is entirely sure what that means.
In any case, magnetism does appear to be a dynamic effect of the Coulomb Force and could be illusionary in the sense that the centrifugal force is illusionary in a dynamic rotating system. It’s probably due to some finite propagation speed of the electric field which gets messed up once it’s no longer spherically symmetrical after Doppler shifting. So, you can still kind of “eliminate” magnetism conceptually with relativity even if you measure all particle dynamics in a single frame, but dynamical effects are harder to model and working on non-spherical fields only complicates it further. Introducing magnetic fields works because the system obeys Lorentz symmetry, which reduces to Maxwell’s equations in a single frame. Needless to say, monopoles cannot exist, even in principle.