I suspected he needed a major change of the LWMesh stack, this is a very tough job.
Non necessarily. LwMesh has enough APIs for you to implement everything from the application layer. You will basically bypass most of what stack is doing in the process, but it is not all that important. It all depends on your general algorithmic and programming skills.
Since you only have one data sink, your task will be relatively simple. There are three basic things you will need to figure out:
1. Network commissioning. Since your network is more or less static, this step may include original route discovery.
2. Routing. Again, with one destination, the task will simplify a lot.
3. Sleeping and synchronization. This is probably the hardest part.
Here are some things I would do if I was working on this project:
1. Do not use regular routing algorithms.
2. Use tree structure instead of mesh. This will simplify routing.
3. For sleep and synchronization reasons, make intermediate devices accumulate data from all of their children and pass it along the tree. You will save on traffic and routing.
4. Each device will have multiple awake intervals - one for communicating with each child and one for communicating with the next router (as a child of some other router).
5. Time intervals will have to be assigned by the central node, and maintained autonomously.
This is a very brad picture, there are a lot of details to take care of, but it is not beyond abilities of any reasonable engineer. Just think though the algorithm using only one primitive - each device can communicate to other devices in RF range, no routing is available. And you will figure out what needs to be done exactly pretty fast.