Give it a try.

If traffic or timing is bad on the way back, do some research ahead of time and take the green line along the 105 and watch the traffic sit!

They used to have D'Land busses (not owned by D'land, just logo'd) that cruise the terminals. Seems pretty painless to jump on one, then get off at the park. If you have a long flight after LAX, then tire yourself out as much as possible.

If you choose to beach it instead, I would suggest Hermosa for a combination of decent eats and good layout. All other beaches are less "centralized" even though all are nice.