Just brush off the loose dirt first. Then gently wipe it down with plain soap and water. Windex tends to kill the glossy finish of bakelite.
The reason that Windex "kills" the glossy finish is because it has a small amount of Ammonia in it. The ammonia serves to better break down the grease n' grime and simply cleans deeper. You do have a point though, but I prefer to put that gloss back on there after I clean them up!
Yes, I am not too worried about buffing the finish back. I just can't wait for it to arrive so I can get started! Hopefully, the dial won't be a huge problem - I had had great luck in the past on AE dials dropping them into watch cleaning solution in the Ultrasonic Cleaner, then re-lubing them. It will also need new cords, which I also have coming. Hopefully it won't get damaged in shipping - if it was packed the way I asked, it shouldn't be. Aw, heck, the dirt will hold it together

It will be a great little project, and I am looking forward to it. It had been a while since I had a complete refurbishing job to do, and I will finally have an AE34 on display!
While most of the phones in the museum are NE, I have a special love for AEs, as I grew up in Brockville, Ont. where both the old Phillips Electrical works plant then the new GTE/AE were located. My first collection when I was young was all AE. I had that collection until I went to college and Mom and Dad threw them all out, thinking they had no value! It wasn't their decision to make, and it will always be a bone of contention for me.
So, it is a matter of catching up and trying to bring back at least part of that collection. Terry has been a wonderful help with newer AE models for the museum, and I have been able to pick up AE 40s and 50s, and other earlier AE phones.
I have an original Phillips Electrical Works subset I found last year, and am still looking for one of them with the handset mounted atop the subset. They were a dime a dozen when I was young in Brockville!
So, that is why I love the AEs so much, and it is so nice being able to share them with others through the museum!
Dave