Many options, but depends on the look you're trying to achieve.

Can we see pictures? What kind of look are you going for?

Here is a photo of one of the beams. I would like to wrap and stain them. And would like no visible seams or joints.

Here are a couple more.

Get a faux finisher up there.

Do you mean a painter

Yes.

I used furniture grade plywood because I knew I was going to paint it white. No seams or joints.

"No seams or joints."

How is that possible?

If you're going to paint them, any joints can be filled to appear seamless. If you're going to stain them, probably the best you can do is to miter the edges. You'll still have seams but they won't be as visible.

I put a grove down the lower part of each of the new box so that the bottom part of the box would fit nicely into it. I guess you would call it a joint or a seam but unless you are bending one piece of wood, there's going to be a seam. Just make it look pretty.

You could add brackets to hide any seams there are lots of options besides just painted wood. We ordered custom brackets to hide the middle seams as we could not find boards long enough in our area and price. Wood is from building that survived the great Chicago fire. Husband mitered boxes from wood to cover our LVLs.