After much contemplation, I think you may have a need for a stuctural engineer.
Here is my thinking on this;
In order to have an outside, load bearing wall, bowing out, I would think an inside load bearing wall, may have been removed or never built!
I believe the outside wall is bowing because it can't handle the weight of the structure.
In order to resolve your problem, you should bring in a pro that can add up all of your loads and determine what you options are.
The cost may be a few hundred bucks, (depending on your area), but it is well worth it to get the right answer.
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