Thanks for your spot-on comments, Jay.
Hemlock: There is a 10x12 option (with an addition) shown on page 141, and you only need two bents and can keep the original sizes. No snow load to speak of in Tucson so even better.
One problem with going to 6x6 posts is getting enough room for joinery where pieces come in from opposite sides at the same elevation, but two bents instead of three and staggering the joints gets rid of that problem.
Yes, a middle bent with tie beam would be good as much to keep the 6x6 plate from bowing out with roof spread (gets worse the lower the pitch) as much as gravity load support. Tie beam at 6x6 would probably be OK with braces under it and no loft.
Are the 6x6'x nominal or actual dimension? You might be losing another 1/2" if nominal from the lumberyard.