That’s up to you, I know I wouldn’t. Draining and filling (myself) the differential because of the groan is my limit with this car.
A second opinion at another dealer would be on my list, if you’re truly experiencing the shudder.
As far as A techs go, I chuckle at the reference. So what’s that mean, everyone else sucks more than him? He has spider senses and can feel vibration more than you?
Recently, an “A” tech was asked to install a single piece aluminum drive shaft in my stang. 2 hours later I’m being asked where I bought the driveshaft (ford racing) I’m then told they can’t install all of the bolts, so if I want it done, they’ll install just 2 bolts of 4 necessary bolts and I can sign off on it (said by service manager)
The problem, which I showed the “A” ford tech (mind you, I’m not a mechanic) He tried to start 2 of the bolts through the u joint while the joint was parallel with the differential. Jesus, we’re not talking about a rubics cube here, 2 minutes for me to figure out.
With that said, get second opinion, why pay someone for something that your warranty should cover? You’ve already paid..