I think there are four lessions to be learned from this experience.

1) Check in the human bags FIRST. That way as soon as the dog was done, you'd be ready to roll.

2) If it is a requirement, suggestion etc. to be there two hours early, don't take a flight 1 :30 after they open. Or get there BEFORE they open at 5am. Not begin looking for it. Although, I agree you should have made the plane easily, and they should perhaps check your bag when you check the dog (I'll suggest it to CO). You did kind of back yourself into a time corner on this one. You only allowed 1 1/2 for a bunch of complicated stuff.

3) Use the Kioski to check bags it's much faster than the elite line.

4) NEVER check bags. If it doesn't go in a carry on... you don't need it. My number one rule.