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

Well all my fussing was hardly worth it. The covering and molding suggested by the contractor looks great.

Here is the beam now. Thanks for your suggestions.

Sue

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