The figures that I saw came from a 2012 project study report on the I-80 express lanes. I found it on an internal Caltrans website so I can't provide a link to it. However, I have attached the schematics for you. The figures also showed realignment and reconstruction of numerous interchanges in Vacaville. I don't know if those were all going to be done as part of a separate project or if they were going to be part of the express lane project. The drawings do not show where the new alignment of I-505 would have tied in with the old. I could not find any other information on the realignment, so I assume it was just an early conceptual proposal that never moved forward. It was interesting to see what they wanted to do though.
As for the express lanes themselves, MTC/BATA has the legal authority to develop and operate the lanes. They have arranged for STA to handle the development of this particular facility (probably in exchange for a portion of the toll revenues). Caltrans will not operate the lanes but they are still part of the state highway system and as the owner/operator of the highway, Caltrans does and will continue to play a major role in their design and their operation. This is how most, if not all express lanes do and will operate in California.
Here are the images of the proposed changes to the 505/80 interchange.
https://flic.kr/p/MU38sS - showing beginning of new Orange Drive I/C
https://flic.kr/p/M7xVMe - showing the Orange Drive I/C
https://flic.kr/p/N5dKnk - showing the western half of the new 505/80 I/C
https://flic.kr/p/MU3mWA - showing the eastern half of the new 505/80 I/C