Attempting to fix a bad spot on the roof will cost you more time and money and patients that you'll want. Here's a very simple and easy solution.
Do not rip anything out.
Simply drill a small hole (or maybe several small holes) and get a several cans of the foamy "Stuff" and begin pumping it through those holes.
It will fill up any air space, and seal tight any water intrusion. And because it dries like styrofoam, it will add some extra strength and support to your roof, and it weighs almost nothing. Believe it or not, this stuff is great!
When done, just put a bit of good tape over the holes you've drilled. If you've used the foamy "Stuff" right, it will probably come out of the holes you drilled and seal them tight. A bit of tape will just make it look a little better and protect anything from getting under (your rubber roof, if you have one).
Doing this, you will not have to tear anything apart. I've used the foamy "Stuff" on everything from sealing a turn signal assembly on a truck when the plastic holes broke out (which lasted 10 years), to sealing cracks around windows, to sealing the concrete cracks around the foundation of my house.
Many years ago, my mother had a rotten spot on her roof (near the edge). I pulled off as much of the rotten wood as I could by simply lifting up the shingles. I then pumped that area completely full of the foamy "Stuff" and simply put the shingles back on top of that (no nails either). It lasted 15 years. She had other shingle loss one Spring that pulled off a bunch of shingles. Insurance paid for the repair, so she had them finally replace that spot with lumber. They actually left the foamy stuff there, and put a thin sheet of plywood over that spot and nailed them down. That was 30 years ago!
Really, this is the simplest and easiest way, and probably lest expensive, and it will work.
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