I had no idea that electromagnetics had so many relativistic components! So, correct me if i'm wrong, but let's say you're running towards the charges and observing an electric field:
There is one true underlying reality in regards to their actual state. To arrive at that state, various observers at various speeds will view differently rendered versions of the same event, witnessing varying proportions of electric and magnetic fields in use (depending on their speeds?), which all reconcile the event with it's true mathematical reality, where the specific nature of the "reconciliation" is based on their frame of reference?