The compatibility of the Grand Tack hypothesis with the "core-warping impact" theory of Jupiter's diffuse core
I think this question might trigger more an open-ended discussion, than a definitive answer, but let me try my take on it.
Firstly,

Is it more likely that one of these collided with Jupiter itself at the head-on angle needed for the core-warping collision?

In order to collide, a co-orbital configuration is more favourable than a orbit-crossing encounter at high eccentricity (as seen in Liu et al., extended fig. 2), but their 'high angles' don't quantify high eccentricities properly. This is because in their simulations, all planetesimals are initialized at circular orbits, with initial distances of 5-10 mutual Hill-radii (their k parameter).
Why I think they didn't properly compare apples with apples, is because usually an eccentric planet would have more kinetic energy than allowed in their simulations, reducing the collision cross-section.
This would lead to drastically reduced impact rates at high angles, compared to the data they show. Furthermore in the early scattering scenario that you propose, most planetesimals would be of too low mass to trigger the core mixing.
The mass required for the impactors is, I think, the major point why the two scenarios are not compatible. The initial conditions for the impact scenarios are those of 5 densely packed 10 $m_{\rm oplus}$ planets, of which one undergoes runaway gas accretion and becomes Jupiter. Those conditions are explained to arise due to oligarchic growth. For the 5 planets, this means that 50 $m_{\rm \oplus}$ are packed in a region of 5 AU size. This is already 1/3 of a median class 0 disc mass, and it necessitates a 100% high efficiency when translating pebbles to planetesimals to planets.
Seeing those numbers lets me strongly doubt the realism of the initial conditions.
Concerning the other part of your question,

The few million years&quot; timescale is quite vague. Does anyone know any additional detail which might suggest the impact occurred prior to the Grand Tack's timeframe?

The few-million years are coming from a certain amount of cooling and compactification that is required for the impact to successfully mix Jupiter's envelope. Hence, the impact should not have occurred prior to the Grand Tack.
Taken both those things together, the cooling requirement and the mass/compactness of the initial conditions necessary, I don't think both scenarios are compatible.