I have an interestingly similar problem. I need to calculate a route length very accurately which spans multiple UTM zones. I need to account for projection error, elevation, and curvature of the earth. I still have yet to find a way to calculate 3D geodesic length in one or two operations. I have done some initial experimentation on the effects of earth curvature on length and can tell you that the length adder is very small compared to the length added by elevation.
For your particular problem I have a couple of recommendations. You are incurring alot of geometric error using South America Equidistant Conic, despite it being equidistant. Your distances and drive times will be way off. Here's what I would do:
1. Calculate a route ID number for all routes which you need to estimate.
2. Split up your road network by UTM zone (reproject each to the appropriate UTM zone; using only South zones is OK so you dont have to deal with another split at the equator).
3. Download SRTM 90m DEM for your entire project area.
4. Run Add Surface Information on each UTM zone road feature class using the 90m DEM. By doing this we can ignore geodesic length adder. Make sure to check on Slope Length.
5. Merge together the split up UTM zone feature classes back into one road network feature. Keep SlopeLength field and dont change it.
6. Run summary on Route ID and check on Sum for the SLength field.
7. Ta da, you have a table showing the accurate slope length of all your routes in one table. This can be joined back to your original single roads layer and you can calc the accurate length in that table for other use.
Hope this helps.
Lee