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Without measuring all of my guitars, I'm guessing that the amount of space between the outside strings and the edge of the neck must be pretty close to half the distance between the strings.
Very rough, but a reasonable estimate, I hope!

That would mean that you would divide the neck width by six for the spacing on a six string (i.e. 5 full widths between the six string, plus a pair of half widths outside both edges). For a seven string, apply the same rule, but divide by seven. The flaw here (not counting my assumption regarding the edges!) is that the spacing between each string being the same means less picking space between the fatter bass strings than the skinnier treble strings, FWIW. Anyway...

For a 1-11/16" six string, that calculates out to 0.281" center to center for each string.
For a 1-5/8" six string, that calculates out to 0.271" center to center for each string.

For a 1-7/8" seven string, that calculates out to 0.268 center to center for each string.

Basically, using all my potentially flawed assumptions, there's not a whole lot of difference between your 1-7/8" seven string spacing and a vintage 1-5/8" six string.