Jimmy…
There’s quite a bit of parking spaces all around Quivira Basin. I’ve never seen it completely full but I try not to go there during the summer on a Sunday or a Holiday. You’ll probably need to get to your picnic area early (6am-ish) to snag a good spot. If your friends get there too late and can’t find a nearby parking place, they can always pay to park at the Hyatt on the north side. As at last resort, there’s always parking on the sand bar just west of Quivira Basin (#6 on your map).