Would it be possible to swap a differential from a 4.6L GT to a 4.0L V6? I've been thinking about doing this because it has shorter gearing and an lsd which is a win win in my book. Please tell me your thoughts and any tips that might help. Thank you.

 

The rear axle is a direct swap, other than changing to the cobra flange so the V6 driveshaft will connect.

You can't just change the differential because the V6 from 2005 to 2010 is a 7.5" rear end and the GT is a 8.8" rear end.

If you get a rear end from a 2011 to 2014 they are all 8.8"

 

Yes, at the junkyard I stumbled upon an '09 GT with 3.73 gears and swapped it into my '07 V6, no issues at all.
The arrow points to the Cobra flange that was installed to connect it to the V6 driveshaft.
The lower gears really woke up the V6 and now I don't have that annoying right rear spin every time I make a turn from a stop sign.