...Mac's suggestion for replacement of the beam and the methods suggested are spot-on.
Assuming that everything else, including the ledger attachment method, flashing into stucco, etc....is correct. I agree.
It's essentially the same concept of supporting floors in a home, when replacing structural supports.
Well...I took the advice. It actually wasn't as bad as what I thought and took less time than what I thought and expected.
I have to say, the cat's claw I had sucked and sucked bad. That's what I dreaded because the nail-pulling was an enormously time-consuming task from past experience. I went down earlier yesterday morning and bought another cats claw hoping that maybe a newer one would work better. I bought a different type one. Sure enough, then I went to use it on the other part of the deck that I am just re-doing with a bigger beam (i.e. this is the other one for a cantilever for a bay window that was approved for a 2X6 beam but it should have been a 2X8.) Tearing down that beam with supporting the joists temporary with a 2X4. I've put the 2X8 in. This went so quick and easy I just said, "what the h3ll" and made the adjustments to the main beam. A quality cats-claw makes a world of difference.
I used a palm nailer (as I did before too) which definitely helped. Poor ol air compressor I have; its just probably yelping for rest with all nailing and the lags. :-( Poor thing.
I'm going to call for an inspection tomorrow and really hope the inspector approves this, now. The beams were the only item (albeit a very critically important item). I will respond as soon as I possibly can (IT related work-items (training other experienced IT professionals - what fun) on the immediate to-do.)
Thanks all for the information. I know there was some disagreement on some aspects. I know there are good licensed contractors and good inspectors. My experience must have been on the not good contractors every time unfortunately, which has left some resentment. But I know there are good ones out there and I've seen their work and it's excellent but it was too late. I just need to give them another chance when I feel I'm in too deep and need help. My inspector is good and a very nice guy. But all-in-all, thanks for the persistence and it's very, very much appreciated.