my soul is exterminated

I wouldn't say I cried... More like a gut-wrenching horror. By only intending to help, the first Doctor made the Dalek's last moments hell. Is it what he wants to remind himself of, that his mercy was actually received like torture? And the more he comes, the more he realises how much the Dalek must have suffered from his last display of compassion, and his first clueless visits?

Poor Dalek, even them don't deserve such torture, even if he was, in a way, responsible of how he perceived the Doctor's behaviour.

Did I have feels?
Yes.
Did I cry? I wish, but I try to not cry.

Could you be a desendant of Moffat, where what he does is write all your feels and loves onto a script, shreds your emotions, takes the shreddings and sprinkles them over a stew of plots, then, AND THEN... forces you to eat the stew very slowly, and when you're done, he hands the script back to you, in perfect condition?
Yes.

And I've been sitting on that for a while.

This is an exceptionally well written story, a really interesting timey-wimey scenario you thought up there. I may did not cry over the Dalek but I did feel sorry for it in the end after everything the Doctor put him through, partially without even realizing it. After finishing it, I read it backwards from the Doctors point of view, his actions and constant pitying looks make much more sense that way.