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Treating the eyepiece and Barlow as simple positive and negative lenses yes it it feasible to compute the required separation but it is necessary to know the focal length of the Barlow as well as that of the eyepiece. Since both are actually comprised of several elements it is necessary to determine the nodal points and use these to set the separation - which is non-trivial because you will need an optical bench to find the nodal points experimentally.
A rough way is to assemble diagonal + Barlow and eyepiece the way Takahashi intended and measure the spacing with a ruler along one side parallel to the approximate optical axis, maintaining this separation should achieve what you want.
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