I don't see how the fact that the graph results from a voronoi diagram substantially changes the problem. You have a graph and want to do a k-cut, where k is the number of your workers. Instead of minizing just the cut, you also want to make the partitions equal in size.
There is a ridiculously simple heuristic for k-kut. Pick an edge at random and merge the nodes at both endpoints. Repeat, until desired number of components is reached. Try again from the beginning, until bored. Output best result.
This works, because expensive cuts have lots of edges that could get picked, while cheap cuts have few and are therefore selected less often.
Normally, the problem is formulated with edge weights, and edges get picked at nonuniform probabilities, scaled by their weight. If you would instead pick edges with probabilities scaled in such a way, that it favors equally sized components, it should be possible to find a heuristic that gets good results for both minimizing cut size and spreading nodes equally.
I'd suggest to weight the edges according to the number of nodes in the original graph that the resulting node would represent. Edges which represent multiple edges in the original graph, should also get higher probability (their weights start at one, but must still be aggregated on a merge). The resulting probability to pick an edge would be: (number of edges in the original graph the edge represents) / (number of nodes both endpoints represent in the original graph, combined). Off course, this needs to be normalized to 1.
In this way the components would grow at roughly equal speeds, and components which are well connected are merged together with higher preference. I just tried this with a small pen and paper example, and it seems to actually work out just like that.
Depending on whether your problem suffers more from unequal work loads or too much network access, you can tune the probabilities to prefer merging due to high edge count over merging due to low node count or vice versa.