This is a quite interesting problem.  I have an idea, but I haven't
tested it so I don't know how well it would work.  Once you have a
spline of the right length, you can use Peter Popov's method to place
the points equally along it, so the problem, as you said, is finding a
spline of the correct length.  My idea is that you could take your
starting spline and calculate its total length (using an approximating
sum).  Then take how this sum compares to the desired length, you could
then move the control points toward or away from the line connecting the
endpoints of the spline and repeat the process until the spline has a
length that is close enough to what you want.  The advantage of this
method is that you can change exactly how the control points are moved
to get an effect more like what you are looking for.

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