Does this ceiling joist layout look structurally sound?
The roof framing really helped. Since according to the code book, you can have limited storage in the attic with the framing you specified, I would still tie all the framing with a layer of subfloor, which in turn can be used as storage. This is because the hips will exert an outward force to the outside bearing walls. There may not be a real issue with this since everything is tied back to a triple beam and tied to an interior wall as well. I would still run plywood in the attic anyway. It will make a great work surface while framing the roof too. This will mean the beams will need to be made of 2X8s or LVL's, this is engineered lumber that measures 1 3/4"X7 1/4"X any length you need.
IMHO, the 2X12 beams are way much bigger than they need to be. There simply is not that much live load for them to carry. The wall that is under the ends of the joists that are near this beam can have a beam under it, to help carry what little load (stored items) it may need to support.

You may want to consider adding a beam at the other areas where the rafters will cross over the ceiling joists, so that short joists can be tied to the rafters like the rest of the house. Another alternative is running the beam at the ceiling level the same as the hip rafters. LVLs will help here too. This would eliminate the long one that goes all the way across.

The only 2 issues that I see is where the vaulted ceiling will be and the access. The possible plywood floor may eliminate the need for the joists to tie through. The other is the lack of collar ties. they in essence  help break the span of the rafters, since one rafter when loaded will try to push against the other, but the other is trying to do the same. Purlins with knee braces may do the same also, but they will bear on the ceiling joists, may not be a good idea.

That I know of bridging is not required in ceiling framing, although it could be added.
A final note on the access and vaulted ceiling, the code used to require ceiling joists at 32" OC (joists on every other rafter) for conventional framed roof as a minimum. With the engineers blessing he may allow the openings with the plywood deck around it to pass.

A little over sight on my part. There will be room needed for the insulation, so the plywood deck will need to be high enough, depending on your climate zone to get anywhere from R-30 to R-49 to be run under it without compressing it. So, 2X12 beams will work with an overbuild the get the 2X8s to the same height with 2X4s that won't work nowhere else, crooked, twisted, cut too short, what have you.