A321 Captain reported executing a go-around after encountering wake turbulence from a B777 on the takeoff roll on the same runway the A321 was close to landing on. During the go-around the A321 again encountered wake turbulence from the B777.

Narrative

Approach Control was keeping us fast all the way in on the arrival and approach to Runway 25R; and then assigning 180 kts or greater until the final approach fix. It was a clear VFR day with Runway 25L closed. They switched us to Tower at the fix; and first thing Tower said was slow to approach speed. The A321 doesn't slow the best when going down the glide slope. I was using gear and speed brakes to slow; as Tower was clearing a 777 for takeoff on our runway. Tower asked if we couldn't go any slower as we were still trying to slow; and cleared us for landing. The 777 started takeoff roll about the time we passed 500 ft. In the flare we encountered nominal wake turbulence; but a lot of extra lift. Our aircraft climbed and would not descend. After passing 3;000 ft. down the runway I initiated a go around.As we were executing go around procedures the Tower Controller was asking us for information like why we were going around. I started maneuvering a little left of the runway center as we were getting wake turbulence from the 777. Then the heavy 777 start a left turn so I started sliding to the right. That got the Tower Controller excited (probably worried about departures off 24L) and Tower told us to turn left immediately to heading 190. I was not turning toward the Runway 24; but just getting outside the turn of the 777. Tower's directed turn to the south then took us back through the wake of the heavy 777.Controllers need to not focus on how we are messing up their traffic pattern or why we are rejecting a landing; and focus on how they can help us. We don't do rejected landings very often and it can be a handful especially when dealing with wake turbulence. I don't think Tower should have clear the heavy for takeoff when we were 4 miles out doing 180 kts. Maybe Tower didn't know we were so fast. Maybe coordination with Approach Control should be better. It seemed Approach Control was trying to create space behind us for a takeoff. Tower seemed intent on getting the heavy off in front of us. And there was no other aircraft in line for takeoff.Do not clear a heavy for takeoff on same runway where an aircraft is inside the final approach fix. Ensure Controllers understand the A321 does not slow down as easily as the other Airbuses. When a runway is closed at LAX and they are using same runway for takeoff and landings; it is more critical that Tower and Approach Controllers work together to coordinate the flow.