Hi there, thanks for the post. My initial suggestion is that if you do want to add a faux beam at the peak, I'd also include side beams to make the whole space more consistent. Keep in mind, however, that based on these photos, I think that adding the beams would visually lower the ceiling even more. I wouldn't add the beams at all, but would rather think of adding skylights. This could be a bigger expense, but something to consider to make the space brighter.

Skylights would be awesome and enhancing.

Short of that: you have a very interesting structural elements with that accent wall - play that up to add interest.

Consider painting the upper triangle back wall a deeper color; from what I can see from the photo I think Rockport Grey or Bleeker Beige or Revere Pewter would do the trick.

Also, deepen the shade of your window panes to the same shade as the above mentioned wall colors to help tie everything together.

Lastly, consider a much larger area rug in an anchoring color. Meaning the rug needs to reach the entertainment area and extend to the left door jam.

We have somewhat the same vaulted ceiling and I was considering the same thing with adding one beam. What did you end up doing?