...as a justification for Paul's indifference about an earthly Jesus, which would make stronger your case for the absence of references to crucifixion in Acts's Paul's trial as expected by a historicist author.
But dr. Carrier points out that Paul, in 2 Cor 5:16, refers to "our living no longer 'according to the flesh' but according to the spirit", not at all to a Jesus lived in the flesh from the seed of David.
Hence, it appears to me that you are unable to make a case, based on Paul only, for the apostle being indifferent about the crucifixion of Jesus, when in Acts the crucifixion itself of Jesus is not mentioned, during the Paul's trial.
where is the crucifixion, here ?