We're on the way to a happy ending.
It took multiple calls, but ultimately I ended up speaking with someone in management at Juniper Bank. She said the reason for the mixup was that I had been given a Platinum Visa instead of the Signature Visa. I pointed out that there was no way to specify one over the other.
She called back after some more investigation and said that she would credit me the missing 2500 points for the double points on the first $2500 of purchases, and the missing 7000 points due on the $10,000 balance transfer. She said I would be getting a Signature Card to replace the Platinum Card.
As of today, I have received the Signature Card, and I received a bill indicating that there would be a 9500 point bonus adjustment, however those points have not yet posted to my A-Plus Rewards account. I'm fairly certain that it's only a matter of a few more days.
Most significantly, she thanked me for pointing out the inconsistency in their advertising vs. what was delivered. She said an internal investigation would be forthcoming to fix the situation for others in the same boat.
Thanks to JoeFlyer for providing the critical information that supported my argument!