If the map requires the attackers and defenders to manage three separate payloads that run concurrently, it would split the action up in to three areas. It would be a bit like those CP maps that have three CPs that can be captured in any order, and once a team captures all three, they win. But it would be a roaming A/D model.
It sounds like a good idea, but I'm concerned that it might split the action up too much and make the game a bit too quiet. Perhaps two payload carts would be more suitable. You could have the tracks move between being close to each other and at a distance, to offer variety. Just make sure the map is designed so people find things easily.
The mini capture points are good for keeping a match short, so you don't have to set a really long round time. And they also help to encourage people to push the cart. You should incorporate them, but think about how they would affect the game. Maybe, if you had one track which was 'easier' for the attackers, the mini capture point would be at a further distance. While, the more difficult track's capture point would come sooner.
Alternatively, you could give each track its own set of capture points, spaced out in roughly the same distances on both tracks, and each would add time. Or, only the first point to be hit, in a parallel pair, would add time, then disable its brother on the other track. It's interesting.