Spinnor said:
Can I think of the near electric and magnetic fields surrounding the antenna as made of strings moving in space-time, being emitted and reabsorbed by the antenna?
Yes, but to be precise, it's a quantum superposition of such emissions and absorptions.
If you think in terms of quantum particles, electronic and electromagnetic phenomena can be understood as superpositions of processes involving the interaction of spin 1/2 and spin 1 point-particles. A charged particle like an electron is surrounded by a cloud of virtual photons and that is its electrostatic field, a propagating electromagnetic wave can be resolved as a superposition of photons of definite momenta, etc.
In principle, the string picture just takes the point-particle picture and adds extra, high-resolution detail. In the particle picture, a particle might be just a pointlike object, at a location in 3-dimensional space, with some associated quantum numbers. In the string picture, the single "location in space" becomes a multidimensional space in itself - the shape of the extra dimensions at that location in 3-dimensional "macro-space" - and the "type of particle" is revealed e.g. as one of the many distinct ways that a string can be placed in those extra dimensions; and something like "electron emits photon" is really e.g. "string in one corner of the extra dimensions wobbles and emits part of itself, which takes up residence in another corner of the extra dimensions".
That's a little vague, but if we picked a particular string model of particle physics, we could be completely precise about the shape of the extra dimensions and about what string configurations correspond to an electron, a photon, or an electron emitting a photon. Topologically, it's simpler than your sketches - the emitted string just buds from the parent string and completely separates from it. What you have drawn resemble "string junctions" or brane complexes that might be relevant for baryons (multiquark states).