ptb, it looks like Ron & I are on the same page. Since your 4 x 4's are already cast in stone as it were, you will just have to work around that.
But if you have 2' x2' columns around the 4 x 4's, are the columns not structural? How about a photo or three, that will save us 1,000 words.
Does the column extend right to the top of the posts?
I was going to suggest that you could add a short piece of 2 x 4 to the back side of each of the 4 x 4's (say 2' long with a 45º cut at the bottom end) to give added support. Then you could use your triple 2 x 8 to create the proper beam.
You still might be able to use a triple beam...are the 4 x 4's actually a full 4 x 4, or even 4 1/4 by 4 1/4? Or are they dressed down to 3 1/2". P.T. posts are very often - almost always actually up this way - full size. If that's the case I would sit a triple beam right on top, and add some sort of strapping to each side as a safety measure.
Since a 2x is only 1 1/2", a triple beam is 4 1/2" wide.
Now, the 13' span should rightfully have a row of blocking right down the center of the span. You will be surprised how much that will stiffen up the roof. You will really notice that when you are nailing your roof sheathing, which incidentally, will also stiffen up that roof very noticeably.
Good luck.