It is not uncommon for the EX to try to keep their LBS in the friendzone. The general guidance is to continue to DB! So keep GAL, keep 180ing (self-improving) and keep being emotional detached. I would also highly suggest you do not engage in these texts. Stick to the texting rules for LRT: do not respond to statements, direct questions only. And then only on your own time (not right away) and in as few words as possible. Yes or no questions get yes or no answers.
As you point out with your cognitive dissonance, this can play tricks on your mind. "She still likes me! Maybe she wants to get back together! Maybe I should start pressuring and pursuing her!"
That is a cheeseless tunnel. She is going to keep you in her life to the extent that you allow her too. (I am not up on the details of your situation since it was so long ago, but looking back would you say she always saw you as more of a friend rather than a lover?) Unfortunately, dogs do not live very long (we lost a dog ourselves in March, always difficult), but the silver lining to this is that once the current dog is gone you will have no further need to be so connected to her. It will be a sad time (losing a pet always is) but it will also be liberating for you to really move on.
Remember, if she ever wants to come back as a romantic partner you will know in NO uncertain terms. When she wants to come back you will know, when she doesn't you will be confused.
Sounds like you are doing fairly well, maybe still a bit too attached due to her friend zone antics. See them for what they really are and not what you want them to be.
M(53), W(54),D(19) M-23, T-25 Bomb Drop - Dec.23, 2017 Ring and Piecing since March 2018
