I worked in a retention call center for one of the major cell phone carriers for 8 years, 4 of which as a supervisor.
A couple tips:
1) Understand that this is what the person you are talking to does for a living. Some are better than others but a decent agent knows when you are honestly at risk of canceling and when you are just trying to get a handout. This is why your point about making sure you are ok with option b is so important, if you're not ok with option b, you're not leaving, and the agent knows that.
2) Be honest with what the other carrier is offering. While there are some variables like employer based discounts for the most part the agent knows their competitor's plans and pricing. Carrier X is not offering you a free iPhone 6 plus.
3) Keep in mind the agent knows your usage, so don't say you're going to get X plan from carrier Y when you use far more data than that plan offers. Also don't say you can hardly ever get reception when you're clearing 2000 minutes a month.
4) You're a valued customer, no seriously, your account likely has a value and churn risk systemically assigned and this will often determine what can be offered to you. It may have even determined how the call was routed. If you never pay your bill on time and have 18 months left on your agreement, you're not in the best bargaining position, even if another carrier is legitimately offering to buy out your contract.
5) They are your service provider not the phone manufacturer, and smart phones are not cheap. That really high before rebate price you see on the sign is not made up, thats the retail cost of the phone. On a contract plan what you paid $199.99 for the carrier bought for hundreds more and after factor to the costs of operating their business it's months before they make it up, this is the reasoning for early termination fees and the growing no contract, but no handset subsidy options.
6) While retaining customers is the ultimate objective the agent you are talking with has multiple metrics to manage. They will likely have a few options for you, but they also have an Average Handle Time (length of the call) goal to consider, so they'll play all their cards pretty quickly...the offers they have at minute 8 are the same at minute 58.
7) Be smart about asking for a supervisor, if the agent you are speaking with seems like they don't know what they are doing then yes ask for a supervisor, you'll be sent to an escalation rep (a senior rep with the authority to handle supervisor calls) or an actual supervisor (who has direct reports), they will obviously be more competent...but understand this CSAT, or the customer satisfaction surveys you get after the call are VERY important to a frontline rep, however an escalation rep or supervisor handles nothing but angry customers so their CSAT goal is much lower IF their calls gets surveyed at all so if you're just out for a handout and being unreasonable they don't have the same incentive to appease you.
8) The agent has notes on your interactions, if you ask for a handout every other month, they know it. When you ask for a supervisor they reviewed those notes before taking over the call so if you escalate the call every time they know and for them to give you something outlandish is just going to cause you to escalate more in the future. Which causes more calls to care, and each call has a cost to the company.
9) The best time to negotiate is usual December, or at least right before a quarter ends. Cell phone companies are publicly traded, Churn (amount customers who cancel) is a big metric from them so when they are getting ready to close out a quarter they'll often put some richer offers out there for that final push. Mid December is the biggest for year end reporting and you have the added benefit that other carriers have better offers for the holiday which will give you a more legitimate option B.
I do have to dispel the "southern drawl" thing, telecom companies are huge and operate dozens of contact centers in multiple states and time zones. Generally, when you ask to cancel your service and get transferred you're going to get an American (which regular customer service may not be) but they could be anywhere.
Happy shopping.