What a pleasant surprise to see you make Baba too! The baba in your pictures look perfect. I also make mine with only wild yeast (Camaldoli). I start with a fairly stiff biga instead of a poolish because I want to add as little water as possible. I use a strong bread flour, as the Italian recipe I have calls for 'manitoba' flour. Is that correct?
The recipe itself is nothing special but I believe the process is a little unusual: I too separate the egg whites, but I don't whip them. I put the egg whites in the mixer and add a small amount of flour to make a paste. Then I break up the pieces of biga into the egg-white mixture, which forms a dough. Then I add an egg yolk and wait for it to incorporate completely, then a dusting of flour. I continue on in this fashion until I have no egg yolks left, and only a little bit of flour. With the last two egg yolks, I add the sugar and the salt, respectively. After the last egg yolk, another dusting of flour. Then I add the room-temperature butter in chunks, a few at a time. Once the butter is completely incorporated, I add the last dusting of flour.
The reason I do it this way is that I'm told that to create the spongy structure you are talking about, you must never let the fat (yolks and butter) come in direct contact with the flour. I can tell you that I've done this recipe both ways to test the theory and indeed it is true. The resulting dough is so much stronger and 'rope-like' when this procedure is followed. This produces a uniform, medium crumb that is springy.
The recipe as it was given to me was with regular cake-yeast ('lievito di birra'), and I painstakingly converted it to use wild yeast. I would be very interested to learn how much yeast you use, how exactly you use the poolish, and any other techniques and procedures you could recommend. My email is fabtheman (at) gmail (dot) com, if you don't feel comfortable posting your secrets here.
P.S.: Living in Canada I don't get to meet very many people that are passionate about authentic neapolitan pizza AND baba. Its great to know that there's someone else out there who loves the same things I do. At Christmas I also make Pandoro and Panettone; and at Easter I make Colombe. My next goal is to learn to pull the perfect shot of espresso.