Your last statement has me ROFL.
Check-in/greeting experiences can vary. There was no greeter at WL when we went in November, we checked-in at the front desk. I think we were then escorted up to the lounge and they did a very brief tour, but it was very quick and not with a CL CM. I was not given any CL paperwork or anything like that. There's a poster there now who I think said they were greeted out front, not sure where they checked in. So your mileage may vary!
Luggage - yes, you can leave your bags with WL bell services while you wait for your room to be ready. Just drive up and they will help you unload / put on one of their carts. You can then go park yourself or they will valet (for a pretty hefty price, like $20+ a day, but don't quote me on that number).
I have read on here that they do have fridges if any of your food turns out to be perishable - have not done this myself but I've read that frequently. You can leave anything with them, they have a big storage area and people do this all the time. Tipping is usually appreciated, if you are so inclined. When you get your room, just call the bell services button on the phone and they will bring your luggage/stuff up to your room.
I wouldn't think the rental car return process should take an hour, but no personal experience there. WL and the car center are close (the way the crow flies), although a bit convoluted roadways to actually get to/from there. But baring big delays waiting for a shuttle or something, you should be able to do this in 30 mins or less I would think. You could always get an uber from the car center back to WL if you don't want to mess with the shuttle.
Hope you enjoy WL CL. We really liked the new lounge back in November and thought the food was very, very good.