Feasibility of Grand Tack Hypothesis
What you have to keep in mind is that the Grand Tack was devised as a mechanism to generate a truncated planetesimal disc between 0.4 and ~2 AU during the protoplanetary disc phase, in order to explain the small masses of Mars and Mercury (Walsh et al., 2011).
The smallness of Mars and Mercury might be explained differently by pebble accretion (Lambrechts et al., 2019), which wasn't fully worked out yet during that time.
A direct test of whether Jupiter/Saturn indeed migrated during their growth phases, is their Trojan number asymmetry, which is the basis of the paper by Pirani et al., which you quoted. They find that the Trojan-to-Greek numbers should be equal only in the case of in-situ formation, but they are not.
The observed asymmetry is consistent with migration inwards during Jupiter's growth. However, from their work, no clear statements can be made on

where Jupiter's core formed;
how fast the inward migration proceeded; or
whether there was a later outward migration.

Furthermore, the migration rates required for the Grand Tack to operate might be wrong. Recent work coming from people working on migration rates (McNally et al., 2019, Lega et al., 2020) seem to indicate that migration in low-viscosity discs works very differently than what was envisioned in earlier decades. Outwards migration, or stopping, is then easier for giant planets.
Summarizing, many of the puzzle pieces on why the Grand Tack was envisioned and how it worked are currently under active investigation. This is not an issue I expect to be solved soon, as certainty into any of those models would additionally require Trojan asymmetry numbers for Neptune and Uranus, and those are very challenging.