The crawl space case
Wiring in a crawl space (wet location) can be done successfully using a variety of means:
- THWN (pretty much all building wire you buy at the borgs these days is both THHN and THWN) in either rigid metal conduit or schedule 40/80 PVC conduit
- Type UF or NMC multiconductor cables, but not ordinary NM-B, or
- Type MC cables rated for wet locations (i.e. those with an overall PVC jacket and THWN or XHHW-2 internal wires)
However, given the circumstances (i.e. the persistent wetness in the crawlspace), I'd be most comfortable with THWN in PVC and nonmetallic junction boxes down there, with the risers being THWN-in-PVC as well. The main downside, though, is that not only is this an expensive way to wire a house, most "wet location" electrical equipment will not survive being bathed in another storm surge!
Wiring in soffits
The soffit proposal is elegant; however, the main problem is going to be providing access to junction boxes -- you'll need to have blank plates interrupting the molding (preferably on the bottom of the soffit) in order to provide access to junctions:
314.29 Boxes, Conduit Bodies, and Handhole Enclosures to Be
Accessible. Boxes, conduit bodies, and handhole enclosures shall be
installed so that the wiring contained in them can be rendered accessible
without removing any part of the building or structure or, in underground
circuits, without excavating sidewalks, paving, earth, or other substance that
is to be used to establish the finished grade.
Further more, you'd have to use an "old work" type of junction box in this application as you wouldn't have framing members inside the soffit to attach the boxes to. While the 3" by 3" soffit interior should be adequate for cabling, I would not use a conduit inside it due to the soffit interfering with conduit body access. I do not know of any fire code requirement for horizontal cable chases other than them requiring firestopping when they penetrate a firewall; however, as mfarver pointed out, your AHJ has the final say on that, and internal firebreaks in the chase would be wise.
Could a busway be the best way?
Another option for the soffit wiring case would be to use a plug-in, non-ventilated, totally enclosed busway system with branch circuit breakers at the outlet taps and type MC cable run exposed or NM run in surface raceways for the drops/horizontal runs to outlets and luminaires. While unusual for a residential application, plug-in busways offer a high degree of flexibility in layout, and can be subdivided so that branch circuits can be moved with only modest impacts on power to other parts of the house.
There are two drawbacks to this approach, other than it being relatively costly, though:
- A means of access into the soffit that does not damage the soffit would need to be provided: either the soffit side panel could have hinged access panels in it, or the screw system designed so that the side panel can be removed and replaced without causing any damage to it. See NEC 368.10(B) for details.
- You'd need to locate the branch circuit breakers at the tap-off points -- while this doesn't limit the height of the busway, as per NEC 368.17(C) and Point 1 in 240.21(A), there has to be some sort of rod, chain, or what-have-you attached to the breaker handle so that it can be operated from floor level.
In general, there is no problem in screwing drywall (or most other materials or light weight fixtures) into any framing members. This includes 2X studs, beams, steel studs or other variants on these.
There are restrictions on notching and drilling large holes. Dimensional lumber is most forgiving of these modifications, but manufactured beams have especially strict rules about what size and shape holes can be punched through them, and also restrict where they can be put.
Screws, especially thin drywall screws, present no such compromise. If there is some reason why you don't want to screw into the beam, you could use construction glue, but this is much harder to remove if there is some need to change or repair the area.
Best Answer
Depending on what you want and what you're willing to do, one possible approach is to cut the top cabinets on that side to fit around the beams. Lacking pictures as yet, it's unclear how much space that would leave in the top of the cabinets, but if the cabinets are already bought, and the look of the kitchen (new cabinets, full height) matters more than the top having full storage capacity, it can be viable approach (I have lived with "partially occluded upper cabinets" - you figure out what fits up there next to the obstructions.)