Hi
So the problem that you want to solve is, if I understand your description correctly.
What is the closest node inside the start zone to the target that I want to reach?
Does that sound about right?
Currently your agents are optimizing for the shortest total path cost, including the movement cost inside the start zone, which is obviously not what you want.
From this it sounds like you want the same behavior as the user in this post: Find nearest reachable Node with specific tag - #4 by aron_granberg assuming you tag the nodes in your start region.
So you would start a path from where your units’ final position and search for the closest node in the starting region, then you can tell your units to move to that node.
You cannot set the connection cost to exactly zero because that will unfortunately break the algorithms a lot since the path with the lowest cost could for example go around in a circle 100 times and then move to the target and still have the same cost as one that moved to the target immediately. A very low cost is possible, but I would recommend that you try the solution above first.