Cool Hpmer, I'd absolutely love to hear from others who have used this set. I honestly think it's the best wood fired cooking set up ever, but it's probably hard to see that without experiencing it. Anyway, it is a 4" hole up there, some of the videos show an older 30 gallon barrel with a free hand hole in the top. That one may have been a bit smaller, but close to 4" anyway. Honestly, it is very rare that I used much more than a sliver of that opening, so it might be worth while experimenting with a smaller port there. I do think at some point though the system will actually be pulling in there more than exhausting, so there's probably a minimum size that works well.
As for the Weber, I do cut a matching hole in the bottom. I don't know that it's exactly 4", but again, it's close to that size. I do use a ceramic pizza stone for a diffuser, and it does a great job of eliminating hot spots. If you look inside a Weber you'll see that the tabs which hold the grate are actually straps that run down the inside of the bowl. The pizza stone rest on the straps, below the grate tabs, and they space it from the sides about 1/3" or so. That allows the smoke and heat to rise up the sides into the dome. I did try clay pavers, and ceramic briquets as diffusers. Both work well, but it was easy to get a real hot spot if there was a clear shot from the bottom to the food. It's not necessary to buy a pizza stone right away, you could experiment with different diffusers and find something else that works. Also, all the Webers came from the dump due to broken legs, or vents or some other ailment that doesn't matter in this application.
Let me know if you try it please! I'd love to hear how it works for you. Oh, just re read your post and realized you are going for a no barrel cooker. Keep us posted, I'd love to see what you come up with.