Join Date: May 2004
Location: formerly Gold now Diamond, formerly MSY, now LAX, formerly NW, now DL
Programs: Hyatt Plat, Hilton Gold, SPG Gold, Delta Diamond/1MM
Posts: 4,725
Yeah, with that kind of layover, I'd get a hotel room nearby.
Alaska lounge in T6 certainly doesn't have a shower, nor the Virgin Atlantic one in T2.
Check the KAL lounge hours in TBIT (you can walk from the T7/8 where United is airside there in about 15 minutes). I feel like they are open in the mornings and do have showers.