Basing upon the idea that "bullpen logic needs to work backwards", there is an inherent flaw in the "A" vs "B" logic.
On HBD, the "A" pitchers are starting the innings that we set them available for, and the "B" pitchers are also starting the innings we set them for but in less "crucial" situations.
What actually needs to happen is that the "A"s need to be used to pitch out of jams at the end of innings we set them for (or 1 inning before we set them), and the "B"'s need to begin the innings we set them for.
The reason for this is that a B pitcher should always be sent out when the bases are empty, even if the game is 1-run. The reason for this logic is because the only risk, in the moment, is a solo home run. the B pitcher may indeed have a higher risk of the solo home run but it's not much higher than the A and if it happens, it happens.
Any out the B pitcher gets with 0 men on base is a free out that your fireman/closer does not have to get. The B bases-empty outs are "free money" that saves the better relievers.
However, if the B pitcher starts allowing baserunners, he needs to get yanked at the right time. My logic would be - 1 run lead: 1 baserunner (call bullpen 5). 2 run game: 2 baserunners (call bullpen 4), 3 run game: 2 baserunners (call bullpen 4), 3 run game: 3 baserunners (call bullpen 5), 4 run lead, 3 baserunners (call bullpen 4), etc. The number of outs in that inning could also be factored in. 1-run lead+1-baserunner+0-outs would be judged differently than 1-run lead+1-baserunner+2-outs, in the latter logic you could probably still leave the B pitcher in for 1 more batter and see what happens.
The B pitchers can get people out, not as effectively of course but often enough where the risk is still appropriately low.
The A pitchers should be re-defined to fit fireman purposes where they always come in to pitch out of jams instead of starting with the bases empty, and the "setupA" could also double as the de facto "CloserB", and the actual closer B designation should be eliminated completely as an option. That way you could still use your setupA to get those pesky 3-run-lead saves that you didn't necessarily need to use the closer on because they're kind of hokey. You would use your setupA as the 7th/8th inning fireman and you would use the CloserA in the same fashion as setupA, but as an 8th/9th inning guy.
Also, you could make a "call bullpen- 6" instance like leadoff triple, intentional walk in a 1-run or tie game and you need a strikeout and a double play... so where it skips right from setup B to closer even if it was non-9th inning
Under that configuration you could use your best reliever as a closer like you're supposed to according to maths and use your 2nd best reliever as a fireman... kind of a compromise regarding our conversation in the thread.