I have a problem that has been effectively reduced to a Travelling Salesman Problem with multiple salesmen. I have a list of cities to visit from an initial location, and ha
Why don't you convert your multiple TSP into the traditional TSP?
This is a well-known problem (transforming multiple salesman TSP into TSP) and you can find several articles on it.
For most transformations, you basically copy your depot (where the salesmen start and finish) into several depots (in your case 2), make the edge weights in a way to force a TSP to come back to the depot twice, and then remove the two depots and turn them into one.
Voila! got two min cost tours that cover the vertices exactly once.