I ditched double tap after just a few months of riding. I didn’t like much about it, from the super straight brake levers to the imprecise shifting. Mine was 11sp Rival and I haven’t missed it.
It should work though.
You’ve replaced the cable. That’s good. Are you sure you didn’t cause any kinks in the ends? When you rerouted the cable, did you get it properly through the little whoop de doom in the derailleur?
When you changed the chain, did you possibly route the chain outside the little tab on your pulley cage? I did that with Campagnolo and just about drove myself crazy.
Your der hanger is straight, how’s your chain line?
Is the shifter smooth and reliable with just finger tension? Before you connect it?
Is the shifting bad on the work stand or only while riding?
It seems like it should be fine with what you’ve done.
And in the future, don’t wrap the bars until the bike is shifting exactly how you want.