Why would you need to recalculate the entire navmesh once a person reaches its destination? I would only recalc the navmesh once you have placed a building.
I haven't tried it yet, but instead of recalculating the entire navmesh for a terrain, it might be possible to 'add' a new region to the navmesh. Not sure if there is a build in solution for this.
Secondly: If you are using character controllers (thus physics) for movement, consider using position translation. Have a look at this topic:
http://www.leadwerks.com/werkspace/topic/7958-navigation-without-physics/
Thirdly: Although there is some movement behaviour build in, it is difficult to have a solution that does exactly what you need and is finetuned to your needs. You would need to build in your own steering behaviours for your units.
Edit*
I am not seeing any official API calls to make alterations to the existing navmesh. The navmesh system that leadwerks uses (recast) does have this functionality, but there isn't a nice mapping via the Leadwerks API. Would love to see this though.