Needs to be finished all 6 sides so you will be painting or touching up at the very least regardless.

I hate faux beams they always look fake and as for toungue and groove I agree it will be expensive if you can find it at all and I honestly don't like wood ceilings in bedrooms .If you are using pine why not just use the same for this application. Maybe some more info might help.

This is a Canadian company but you may be able to find their product in the US. I've seen this product and it is really lovely with lots of finishes to choose from and 2 different profiles.

Ready Pine.

There are lots of inspiration photos on their site so you can see the finished product - I think it looks great.

You might try Randall Brothers in Atlanta. Am unsure what their shipping cost might be though.

The pine is going to be painted white throughout the house. The ceilings in my bedroom will be a natural color stain.

Thanks for the suggestions!