Say you’ll cancel your service subscription if they don’t give you the package you want.

That usually works. More than 75% of the time, I’d say.

Their call center policy is to haggle with you to try and keep you as a customer.

Ask other people in your local area and use them as a bargaining chip. Point out that your neighbor has the package and price point that you want. Ask why they can get that price and package, but why can’t you?