I am a bit confused by a few items in your post. First off, you say there is an existing header that is 18 feet long, and is composed 4"x10". But in the diagram, you appear to show an existing wall composed of 2x4 wall studs spaced 16 inches on center. If you have a wall, then the existing header is not really a header, it is more of a spacer. So perhaps you can draw what is existing, and what is proposed, or at least show them differently on the drawing.
As to adding a 6 inch header to a portion of the existing header, it is very difficult to fasten the 6 inch header in such a way that it behaves monolithically with the existing header. You need to carry the full horizontal shear across the interface, which is possible, but requires careful design, certainly well beyond any code book. However, it is possible that the existing "header" is strong enough to support the load across the 83 inch opening, in which case the 6 inch "header" you want to add is only a filler, and you may not need any strength.
Rather than spend the money on an engineer, you may just want to go to the county with some photos and some drawings, and discuss your project with them before you submit the permit drawings. They may be willing to help you understand the options.
As to adding a 6 inch header to a portion of the existing header, it is very difficult to fasten the 6 inch header in such a way that it behaves monolithically with the existing header. You need to carry the full horizontal shear across the interface, which is possible, but requires careful design, certainly well beyond any code book. However, it is possible that the existing "header" is strong enough to support the load across the 83 inch opening, in which case the 6 inch "header" you want to add is only a filler, and you may not need any strength.
Rather than spend the money on an engineer, you may just want to go to the county with some photos and some drawings, and discuss your project with them before you submit the permit drawings. They may be willing to help you understand the options.