Thanks to everyone who chimed in.

As a follow up, I made one last phone call into the main AIG customer service line. I actually got ahold of someone who really looked into my claim. She saw that I was supposed to receive a call back several weeks ago and never got one.
She sent an email to the agent handling my claim, her supervisor and the "escalation" team. Surprising I just got a call from the claims agent and she said she does have everything she needs and will be sending the approval over to payment dept and a check should be sent out in 3 business days.
A data point for others filing a claim, it took 7 weeks from the time I filed the claim until I got the first email from the agent that would be handling my claim.