One of the characteristics of IRV is that a round cannot be tallied until after the prior round has been tallied. Maybe there’s a way around that while still somewhat addressing the IRV advocates’ criticism of Score that any support you give to your compromise candidate hurts the chances of your favorite winning.
Suppose we had two rounds of tallying, and the ballot would consist of a Score ballot for each of the two rounds. The first round would eliminate half the candidates. So for that round, the voters could concentrate on trying to eliminate their most hated candidates. They might well vote in Approval style, and maybe an Approval ballot is all that is needed for the first round. An elaboration would use more than two rounds, but the count of rounds would still be fixed from the start, and the counts of eliminations for each round adjusted so that at least two candidates would survive to the final round. Maybe it would go logarithmically, with each round eliminating about half the remaining candidates. Or linearly, with each round eliminating about the same number of candidates, with the possible exception of the last round. Anyway, the precincts could publish the results round by round; there would be no need to wait for a central decision between starting to tally rounds. The calculation of the final result would ignore for each round, the scores of candidates already eliminated in a prior round.