I don't have experience with Comcast TS personally (which I consider a blessing), but I've always found I can escalate myself to T3 pretty quickly, by addressing my problem at their level.
When T1 starts their script, I state my problem. There's usually a pause, and they ask the next thing on their script, at which point, I politely state "It appears your script isn't designed to handle my issue. Would you please connect me to your manager?"
They're more than happy to do so, as keeping me on the line guarantees that they'll have fewer calls handled, which means a worse score at the end of the day, and I've already informed them they'll eventually have to escalate anyway.
I then run through the same routine with their manager, stating the same details, and adding in why the T1 couldn't handle my call with their script. I then ask some technical questions about the hardware they're using on their end, at which point they realize I probably know more about the domain than they do, and keeping this call or dropping it back to T1 is just going to look bad on their report. So they ask me if someone from T3/engineering can call me back, to which I say that would be fine, I expect the call within 20 minutes.
Depending on the political situation that manager finds themselves in, this either results in me getting a call back within 20 minutes from someone who can actually do something, or, 20 minutes later, I call the sales number and ask to speak to someone in customer retention.
I then go through the entire situation again with them, and most of it flies way over their head. They offer me a better deal on X for the next 6 months and apologize profusely, and I turn them down, explaining that unless this problem is fixed, I'm without service anyway, and have no reason to keep paying them when they aren't providing the agreed service.
I then ask them if they could get someone who can fix the problem on the line, preferably someone from engineering. Within 3 minutes, I always have.
Yeah, a one-time test might be easier and faster, but they'd abuse it. This way, you get to play the politics against them. Figure out what each person's lever is, push it, and you'll get to the right person fairly quickly.
One thing with this: make sure you record the name of each person you deal with, and the time you dealt with them. Sometimes, asking for a direct line you can call them back on works too (at each level). That way, if you get "accidentally" dropped into the voice system merry-go-round, you can skip the first steps next time and call in where you left off.
Amassing a list of names, times and numbers will always help with leverage on future calls as well :)