Based on your description of the problem, this is what I would do:
Given a vector of lat/lon positions which represents one route, where the distance between points is not evenly spaced. I want to divide this route into N evenly spaced distances.
In order to interpolate on distance, you need to create the distance vector that corresponds to the lat/long vector. Compute the distance from the start of the route for each lat/lon point. E.g. d1 = zero, d2 = the distance from pt1 to pt2. d3 = d2 + distance from pt2 to pt3, etc. This vector is monotonically increasing from zero to the total route length.
Now you interpolate the total distance vector based on your desired distance spacing, then use that to locate the corresponding position in the lat/lon vector. The corresponding point will be bounded by the same index values, and have the same fraction displacement between the bounding values.
