All kinds of possibilities. But,"cost-effective and efficient" leaves out other considerations, perhaps subjective, about living in a home.
You may also mean "rafters" instead of "beams".
IMHO, fake detracts from a home's "quality".
To achieve what I think you mean, a timber framed rafter structure w/ collar ties or structural ridge and SIPs on top would be simplest.

Do you want to build a timber frame home? Those have to be built frame/beams first.

My parents have a lakehouse with large wood beams that were installed after the sheetrock. The installers had to drill large holes through the beams and attach them to the structure. They plugged the holes. They look nice also.

My personal taste is to stay away from faux beams (and rocks). Not having priced our beams any other way, I don't know how cost compare. I do know a true timber frame home is not inexpensive.

We have beams that are structural. They were installed during construction prior to the roof, sheet rock, etc being installed.

During:

The kitchen beams were installed the same way:

Here is a link that might be useful: kitchen pictures