For Turf War, the Tempered can make great use of the left island-There's enough p there to get your Killer Wail charged up twice, so if you can aim well, you can help out your team while controlling a major part of the map. Before trying to get the right island, make sure to take out any enemies, it's really easy for them to pounce on you. (And if you're still using the Tempered, use Seekers to get down to their island, you need to get away from their spawn fast and it'll be easier to fight them off from the island)
In any mode, keep an eye on the slanted conveyor belts and the platforms near the opposing teams spawn. (The ones you would go on if you went right) People tend to want to head for these, and in some ranked matches, you can get up on more of the platforms.
Also, be careful around those yellow crates, I feel like I have a tendency to get into situations where I have a lot less mobility than whoever's shooting at me on the other side.
I've never played any of your other weapons, but if you're interested in trying it out, I feel like the Carbon Roller Deco can be pretty good here. Its main weakness is high walls, which never show up here. Even the grate that usually serves as a perch can be hit by jumping and swinging, and close enough to get a splat in with one swing rather than flicking. Seeker Rush can block off the conveyor belt in front of their spawn for Splat Zones, and Seekers are good for hitting people up conveyor belts that would push you back. Because of the size and flatness of the map, it's also really easy to get around with them.
The Carbon Roller Deco has a bit of an advantage over the Tempered on this map because of its openness. When trying to flick or paint an area, a Dynamo is a bit more vulnerable to hits after traveling a Seeker trail because of its slowness, but a Carbon Roller would have an easier time. I imagine I might be thinking this due to my playstyle, though, I tend to want to get up close, so I don't have the habit of keeping my distance with a Dynamo.