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Home Improvement Stack Exchange is a question and answer site for contractors and serious DIYers. I have built some of the "arches" for a gambrel roof, I know support is needed so the roof doesn't collapse. I would like to avoid having to have support run on the inside so it's a cleaner geometry inside. Trying to brace the roof from the outside as you illustrated will not add any significant structural reinforcement.
In order to analyze the tension and compression in each truss member, the standard practice is to assume the joints do not support any torque loading (aka moment in engineering terms).
In this case I only solved for the tension in member CI, which is what you're interested in eliminating. DISCLAIMER: I'm not giving you professional engineering advice, I'm just trying to help you understand how truss structures work so you can make an informed decision yourself.
If you want to look more into the methods I used, a Google search for 'statics truss examples (PDF)' may be the best place to get started. EDIT: I was at Home Depot last night, and noticed they had several pre-built sheds with gambrel-style roofs.
I am not sure how much roof space you have but a simple solution which would help would be to place a beam between the two lower legs of your roof.
Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site.
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To build a garden shed mark out the area of your slough with wooden Dig the Put shaping sheeting. Is it reasonable to run twin metal straps around the roofing diagonally on the outside for support so the roof is pulled together? Without the metal bands, the front and back walls carry the brunt of the lateral load that the roof places on the side walls. The reason is easier to understand when you examine how the different members in a truss work together to support a load. Since this loading is symmetrical, it can be assumed that the vertical reactions are equal.

I looked inside, and most of them simply had plywood gussets holding the truss members together, with no cross-beams. I was thinking of revising my answer to suggest including the external frame plus a member from A to E and E to J, then a horizontal tension member somewhere in between connecting the two.
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The top members of a truss supporting a vertical load are generally in compression, with the bottom in tension.
For the beginner, I always recommend arbitrarily assigning each member in tension, and if it solves to a negative value, that means it's actually in compression. So if you calculated the total weight of your roof material, you should be able to get a rough estimate of how much lateral force is going to be on the walls.
Although, the larger ones usually only had half of the roof built this way, with a loft to stabilize the roof at the rear half.
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