Patio Doors - dry rot
I have 3 double wide out swinging patio doors (door frames are 60" wide x 94" high [yes, slightly less than 8'] ). These doors face south and receive blowing rain when it storms here in northern California.
All six doors have dry rotted at the bottom - I'm finding pieces of the doors on the patio. The doors are glass with Douglas fir frames painted white on the outside, clear varnish on the inside. I need to fix the dry rot before the doors fall apart.
I'm thinking of removing each door, cutting off the bottom to good wood, gluing a piece of fir to within 7/8" of the bottom, if needed, then gluing a 7/8" piece of teak wood to the original length.
I've looked at door shoes, a door guy said shoes are not normally used on out-swinging exterior doors, but the bottoms should have been finished when the house was built 12 years ago - I don't believe they were, the door bottoms were in contact with the threshold, so water wicked up and caused the dry rot.
My questions are does this sound reasonable and what type of glue do I use to join the teak to the doug fir? I want a permanent (20 year) solution if possible.
Thanks, any comments are most appreciated.