An episode of dynamical instability is thought to have sculpted the orbital structure of the outer solar system. When modeling this instability, a key constraint comes from Jupiter's fifth eccentric mode (quantified by its amplitude M55), which is an important driver of the solar system's secular evolution. Starting from commonly-assumed near-circular orbits, the present-day giant planets' architecture lies at the limit of numerically generated systems, and M55 is rarely excited to its true value. Here we perform a dynamical analysis of a large batch of artificially triggered instabilities, and test a variety of configurations for the giant planets' primordial orbits. In addition to more standard setups, and motivated by the results of modern hydrodynamical simulations of the giant planets' evolution within the primordial gaseous disk, we consider the possibility that Jupiter and Saturn emerged from the nebular gas locked in 2:1 resonance with non-zero eccentricities. We show that, in such a scenario, the modern Jupiter-Saturn system represents a typical simulation outcome, and M55 is commonly matched. Furthermore, we show that Uranus and Neptune's final orbits are determined by a combination of the mass in the primordial Kuiper belt and that of an ejected ice giant.