Starting the Treehouse -- Constructing the Deck

I have selected an oak tree appropriate for the treehouse.  I am a little concerned with the height that the deck will be at from the base of the tree. The tree is about 2 feet in diameter at the base.  The deck will be about 24 feet above the ground.  I have gone up into the tree and cleared out some smaller branches so that I can work unencumbered installing the deck for the treehouse.

I was fortunate to get my hands on some discarded 6"x6", 50 year old redwood beams. They are about 22 feet long.  My first approach was to design a "K" shaped beam structure and then box the "K" in with 2x6's, but once having raised the beams into the tree I have changed the structure to a square boxed in "H" structure.  Below are the pictures I have taken of the first three beams that I have put in place:

I installed the 14 foot cross beam first and used lag bolts  1/2"x10" and 14" to bolt the ends onto the two respective branches.  I had to install a shim under one end to get the beam level. The holes drilled into the beams are considerably larger than the lag bolt.

Next I installed the other two 11 foot beams, resting them near one end on the cross beam and on the other end to a substantial upright branch and to the trunk of the tree, respectively.

I will install one more beam between the last two beams and then cap each end of the deck with 2x8's.