So, assuming you can’t just change the font to a single line version…
You want to pack as many identical circles of as large a size as possible into the region defined by each letter, then find the order of them that works for interpolate to produce the minimum length line or lines.
That’s a nasty problem space.
You could skip the circle packing, use offset to make a much smaller zone in the center of each circle (stop increasing offset if the offset curve self intersects). You can have free floating points in that zone, and use galagapos to find the location for each point to minimize the length of line of interpolation - it would break on the ‘t’ in the example. The galagpos evolution would handle getting the points in the right order as well as lcoation.
You could make each region a mesh in kangaroo, apply each edge as a support and apply gravity. The deflected shape would give you the position of the midline. Just take samples on a row by row basis. It wouldn’t solve the interpolation order problem though.
Any further info/context you could give us? there might be a different line of attack. If there are limited number of characters, a manual solution once with a lookup table might be possible.