I would furr it out and wrap it with drywall (veneer plaster is even better). There is no reason for the beam to expand since it is inside a dry conditioned space and the shrinkage of an LVL beam is unlikely to be seen in the finish work. If you are worried about the shrinkage at the ceiling intersection a simple quarter round, bed molding or apron trim would be far less noticeable than crown molding. I've wrapped multiple beams in a ceiling with drywall with no problems but I always use blueboard which keeps the surfaces flat.

I recommend following your builder's suggestion. The trim board at the top seam is the place to get creative. You should try a variety of molding options once you get the bottom and sides covered with the pre-primed material.
Instead of the flat 1x4, maybe a 2" cove, a 3 1/4" baseboard or casing, or a combination; thin lattice as a backer for a panel molding or rake molding. Limitless options.
Casey

Wrap it in a birch ply and paint it.

Lots to think about.

Ron6519...does that come in sheets 15' long? Not looking for any seems along the horizontal expanse unless there is a way to make it look seamless.

Sue

What was the product you used to cover the beam? Thinking of doing similar