Type III radio bursts are associated with energetic electrons accelerated by solar flares from the lower corona. The standard theory links these emissions to a conversion of plasma oscillations excited by the bump-on-tail instability into electromagnetic waves. Since electron beams can propagate to large heliospheric distances and continue to emit radio waves, the instability must be finely balanced, not to disrupt their propagation (so-called Sturrock’s dilemma). To explain this, many models invoking contrasting processes have been proposed (e.g. quasilinear vs strong turbulence description of interactions between various plasma modes). In this study, we perform 2D PIC simulations of beam injection, propagation, and emissions in a large system without periodic boundary conditions. Results demonstrate that the beam decouples from the excited electrostatic oscillations near the injection site and propagates through the background plasma with relatively small energy loss. Downstream, the instability continues to operate only at the beam front. The main body of the beam between downstream and upstream reaches a quasi-steady state. It may become unstable again where the background plasma is colder or less dense. Background temperature variations affect the beam instability more than background density fluctuations. Radio emissions at plasma frequency and its second harmonic are primarily generated upstream in the region of intense fluctuations, where both classical signatures of three-wave conversion processes and those associated with modulational instability are detected. Our results are consistent with satellite data showing that electron beams often continue to generate type III radio bursts even beyond 1 AU. They illustrate in a first-principle model how a beam state consistent with subsequent quasilinear relaxation emerges shortly after beam injection.