You seem insistent on overcomplicating things that have explanation easily at hand. Hurt isn’t counted because the character relinquished the title for the period of time that he existed. Tennant is only 10th and 14th. The metacrisis Doctor was not the Doctor, they weren’t even Timelord. And Gatwa isn’t “sharing” the current generation. The bi-generation is best explained as time loop - 14 will continue to live and emotionally heal, and at some point will regenerate into 15, who pops up where they’re introduced in the show (ie “doing rehab out of order”). And to your last point, Jo Martin’s Doctor pre-dates the current cycle, which is pretty plainly established by Chibnall themselves, so I’m pretty sure they understand it.
To keep it even more simple, just believe the show runners when they say which iteration is which instead of deciding they’re wrong about the show they are making for reasons that have already been explained.