Hi everyone, we just moved into a house, surrounded by neigbors' properties on higher ground:

This causes occasional stormwater runoff to our backyard and we are planning to make a swale to carry all those water away from our house to the street:

Why not to use underground drainage system?
Because the system is pretty old and partially compressed by underground rocks , reducing the water flow. We consulted two plumbers, both inspected and said so far the system doesn't have any blockage. It can accomodate the water flow from 4 downpipes without any backflow problems, but the compressed system is already at full capacity , so it wont work to install drainage pits in backyard and connect them to the existing system. Unless we spent $2000 to relay all those underground pipe!
How about AG drain?
Yes, it seems very common, though both plumbers said its not suggested because the soil is mostly clay soil and makes it difficult for the water to get soaked into the AG drain pipe. Another reason is, the rainfall can be so heavy pooling on the surface that AG drain wont be effective enough. And they said we need to focus on surface drainage such as installing drainage channel
, but this requires large area of concreting around the house first.
What about other solutions?
After some research, its seems SWALE is another good surface drainage solution. We already dug a small trench, and had some success in divert the water from the left (area with most water) to the right side of our backyard.

Some google picture ideas:


What do we need to do?
To turn a Trench -> a Swale
We need to dig wider and deeper.
What are the challenges ?
1) Even we dug a small trench, the weed spreaded like wild fire and often invades our trench , they are so dense and impede the water flow.
2) The soil can be loose and crumble a little bit blocking the trench
Questions:
1) What type and size of gravels do we need to get from Bunnings to put into the swale?
Type: Ideally it can interlock with each other, so probably need something angular, not round pebbles, and this way we can "walk on" the swale.
Size: Seems we need smaller rocks to "support" the swale and prevent soil erosion? But if we its too small , not sure if this can impede the water flow. But if its too big, we cant walk on them stably. We will lay turf around the swale in future.
2) Do we need to lay weed mat or some mulch in the swale first? Or the rocks will be enough to block the sunlight and prevent those weed from growing.

Video showing the direction we want the water move:
https://www.youtube.com/watch?v=dpLj6qWIFx8
(Looks like a mess. We just moved in. But hopefully we will overcome all these challenges and turn it into a nice backyard without water pooling. You might also notice an old concrete slab, we will remove it with our impact driver.)
Thank you so much for any ideas and advice.