I've been noticing when making tight right turns at low speeds, such as around corners in the residential or office complex, I am hearing a tire chirping in the rear. Is the diff getting lazy and freaking out with what to do with the inside tire? Don't recall having this in the past.
Do not fret Young Jedi. In all actuality, this is a good sign! A nice, tight LSD - or absolutely one with a locking diff, the inside tire will chirp and bark as it breaks traction to "keep up" with the faster rotating tire on the longer, outside of the radius or corner.
This is fine, as when just "rolling along" while pulling into a driveway, around a tight residential corner, or into a parking space where you do more of a 90 deg turn in, rather than a nice sweeping radius type of approach. This will be especially noticeable on very smooth, polished concrete surfaces. So, "corner cuts" for curbing where there is a gutter and handicapped walk ramp approach, in a gas station, or the infamous "squeaky" polished surfaces found in most multi-level commercial parking structures.
If you hear any clunking, or a loud, 'BANG' that shocks you and can be felt through the floor of the car, I would say that you need to add some more "Ford Friction Modifier" to your Diff Fluid, as your clutch packs are glazed and sticking together. The big bang is the sound of it finally breaking free, releasing the tension between the two half shafts spinning at different speeds. A factory clutch type LSD with high miles, low or burned fluid and lacking an appropriate amount of "Friction Modifier" - even, or especially after a fresh fluid change will do this. Not that big of a deal. Add the modifier, in time, it will start to slip as intended and return to normal, quiet operation and a smooth engagement.
A worn or 'Lazy' LSD is one that spins a single tire from a standstill, or most commonly, spins up the "inside" tire as you accelerate through a corner. The tighter the turn, the higher horsepower the car, the more obvious and intense the wheelspin. Some wheel spin is normal, and with a 'tired' factory LSD it is common, especially when running a tight road race suspension and sticky tires. But, as long as the outside tire continues to put a good portion of the power to the ground and provide forward motion, again, it isn't a critical situation. When one freewheels and spins with zero forward push, then the LSD is shot, or you may even have an internally snapped half shaft and not even know it.
I think you are ok. Especially with the addition of recent mods. You may be putting down more torque at lower rpms now and it is just making the situation more obvious. Even changing to a different size or compound of a tire or change in ambient temps will make an obvious difference in one's Daily Driver, to a well tuned and alert driver who knows every intimate smell, feel and way his car reacts to various situations.
My advice; stop dwelling on what the car is doing, and for a day or two concentrate on when, and more importantly where and under what conditions the car is doing this. I would bet that in short order, one or several of the above described scenarios will become immediately obvious.
You can mail your check, money order or other Paypal donation to the address located on my profile page within this forum. Enter the discount code "FreeTechAdvice" for future discounts and BRAKELATE promotional items.