Hello Dr Bert how are things going in Visalia?
My (stock) 85 runs great on the 2.88 - highway or hills (and I drive plenty of mountain roads). I replaced the 3.07 in the '83 300D (now sold) and it ran like it should have from the start. Wow I can't begin to tell you how much of an improvement that made!
If you run a turbo with the ALDA setting mod (I used a copper crush washer under it instead of removing the seal) and the boost lines are not plugged up and (very important!) you have set IP timing to spec THEN the 2.88 differential will really be a very worthwhile swap, better top speed and lower fuel consumption all at the same time. Realizing that Dr Bert has certainly got everything listed (and then some!) perfect, better than spec, I mention those factors because they are important, if you slap a 2.88 into a poorly running (ie. sluggish) turbodiesel you are NOT going to gain anything in fact you may wind up lugging an engine or wearing out the tranny as it down shifts too much, as well as polluting more than it would otherwise.
Oh, yes (personal need) I am interested in finding a low mileage 3.07 for my 220 Gasser. I put the 3.07 out of my '83 300D in it, even though it was a whiner (that was one reason for wanting to upgrade to the taller gears, it was a 3.46 I believe) I really wanted to try it out.
I was told the gasser would bog down with such a tall gearing but as its a strong little puppy with a stick shift it actually works great! Now I want to find a quiet 3.07 diff for it. So if you do find a 2.88 for your W116 please let me know if the old diff becomes available! I can fit a 116 diff in to a 115 or a 123 for that matter. But you need the right spacer rings to fit the half shafts.
DDH in San Mateo

__________________
'95 E320 Wagon my favorite road car. '99 E300D wolf in sheeps body, '87 300D Sportline suspension, '79 300TD w/ 617.952 engine at 367,750 and counting!