Thanks for your offer.
However, I have found out how to achieve what I was looking for.
Here are the steps I took :
1. Import the map into Avid FX (Boris Red, if I understand correctly)
2. Draw the line using the spline pen, with curves and squiggles as desired.
3. Click on "Write on" in the tools menu.
4. Adjust the bezier points as desired as well as the appearance of the line (deselect the fill check box along the way).
The result ? The line is drawn in a linear fashion, taking the length of the track as the duration of drawing.
There you go. Hope this could help others who may be wondering how to do the same thing.