We run our HNL flights out of 69A, in and out. We have our own counters and equipment there, but the gate itself is shared with UA. UA also has counters there, and probably uses the gate for most of the day, since our summer schedule currently has a widebody on the ground at LAX for only about 4.5 hours, from 5:15am to approximately 9:45am.
However, once winter rolls around, we probably will be parking up to two 767s at a time in LAX. The early-AM departure to IAH will most likely be overnighted at our MX facility, brought in by the late-evening arrival from IAH, (unless it continues to HNL, which I doubt) and rolled out to Gate 68 and the HNL arrival will come in at 69A, turn, and board for the next flight to HNL and onward. The afternoon 777 arrival from IAH will most certainly be at 69A, and the aircraft will then operate the return segment from the same gate. Our 757s will operate out of 62, 64, and 68, 737s will go from 60, 62, 64, and our connector bus to American Eagle will continue to depart from "gate" 62A.
And that's the LAX story, the way it's been for a bunch of years, before that; we used to own almost the entire T6 at LAX, those were the days.
And COEWR, I agree with you to a point, I think the 737's are good, especially with our service, and give us tremendous flexibility, but I still miss the days when DC-10's and 757s were the only aircraft (save the 747) that had long enough legs to reach LAX from EWR nonstop. Even then, we had the same number of flights (probably more than we do now), but today we just have far fewer seats than we used to.