Working for corporate, one of my positions was heading the insurance department handling total loss claims. You are abos nuts not to have your GAP and primary insurance company be the same company.
I've seen hundreds of claims where the GAP companies (mostly the ones the dealership sells you) fight tooth and nail and drag their feet in paying out that GAP claim. On GAP claims the GAP company wants your payment history from your finance company (if your late on a payment, get a payment extension they deduct that amount from the claim amount) then they want all the claim info from your primary insurance company including but not limited to the amount they paid out, the appraisal, condition report and how the primary insurance company came to the amount they paid out. It's a simplified process if the insurance company and GAP are the same as they aren't/won't be fighting for the amount that was paid out leading to the deficiency balance.