Firstly the manual actually tells you to only change all 4 tyres at the same time to keep the same tyre depth and overall rolling radius the same per axle. The crown and pinion will wear because of incorrect pre-loading and backlash on the diff due to the different rolling radius of one axle to another.
Secondly the a4 quattro system is a permanent mechanical 4wd system not to be confused with hydraulic haldex types as fitted to S3'S and TT's which is only 4wd when wheel slip is detected. This is why you can get away with different tyre tread depths on cars running this system.
If your current A4 is a quattro then I suggest you read the manual and believe what audi tell you unless of course you know better.
Hi
In the "manual" Audi tell you to go to a dealer at every given chance do you ? they want you to replace your tyres all at once and with them,
Im not stupid i know how quattro and haldex work etc ,
ive been running them for 20 years and even stripped a quattro box and torsen diff ,
there is no way your REAR diff was worn because of a difference in tread depth on the same make model and size tyres ,
are you telling me that with the wear difference between front and rear of quattros which does happen that when the front tyres are getting lower that its going to destroy your torsion centre diff or any other diff for that matter ,
another example in different tyre wear is when you connect a diagnostic machine that will enter the ABS system and read actual wheel speed values,
i have never seen a difference in wheel speeds of any significant amount at any speed with any worn tyres .
As you mentioned haldex also there is a constant between front and rear 97.5% torque goes to the front, and 2.5% goes to the rear under normal conditions this can change with upto 100% lock so they are connected at all times but not mechanically.
Im not being funny here but you seem to be reading more in manuals than you actually have experience with the above mentioned systems .
PS . your pre load and backlash on a diff is not altered by the tyre or wheel speed pre load and backlash are setup when the diff is being built and only alters if diff bearings wear and get play in them you should read that in a manual somewhere .