I'm not from the US but I plan on doing a cross country adventure at some point. Let me ask you this; If my vehicle of choice was a delivery van of recent vintage with an artistic decal of a well known soda brand, would that help with avoiding such encounters?

At worst I could claim to be an Andy Warhol fan, would that fly?

I think the worst thing that would happen is that you'd be asked to leave. I don't think anything worse than that could happen (though don't quote me on that).

I've done something similar one time when a minimalist surfing trip took a wrong turn. I learned that if you (a) have a car where the seat goes down flush with the trunk or hatchback (b) have a good sleeping pad (think REI) and warm sheets, then you can get a great night sleep and look pretty inconspicuous from the outside (no one can see in very easily since you're below the window line).

Also, placement within the parking lot is important, not too close, not too far away.

Define van. Some folks take that to mean the Mystery Machine from Scooby Doo, but locally soda/beer/etc is sold out of giant trucks, semis with trailers.

I think you'd have better odds with a tradesman's van/truck for some obscure service. Not a craft meth heads would be magnetically attracted to steal and fence tools like a plumber. Something unappealing like grease trap cleaning service. Or contents you don't want to screw around with, like an exterminator service.

You'll run into some interesting state laws about commercial drivers licenses, and registration of commercial vehicles. Just because you're sleeping in it, doesn't mean according to the cops that its not a commercial delivery vehicle that you've borrowed or whatever (who cares why) and as such both you and the truck should be licensed to actually deliver sodas for hire. Some states have weird laws. You may even be required to have a business license and business insurance to get the commercial vehicle registration.

A magnetic decal sign applied to a plain old van when stopped might be wisest. Can't be pulled over for something you're not displaying and when you're parked, unless you're about to get a parking ticket, no one cares if you're a properly registered commercial vehicle anyway.

If you are stressed about it, there really are Walmarts pretty much everywhere. There's also lots and lots of campgrounds that are something like $15 a night (you can save that much fueling a smaller vehicle...).

Yes, campgrounds and also backwoods camping. Many of these are government run (state and national parks) and many others are privately run. If you want to live in the backwoods, most parks have rules you need to follow, such as moving your tent every so often, disposing properly of waste, restrictions on lighting fires, and obtaining hunting/fishing licenses (meaning: do not carry fishing rod without a license).

Also, on every highway there are rest-stops and trucker rest areas. Some of these have pay-per-use showers and most have a parking lot you can park overnight in and free toilets.

The national/state parks are beautiful and are very welcoming to visitors.

most cops or security guards will do is to tell you to move on, or harass you. my dad lived out of his car in LA for a while, and he said that you need to pick the areas in which you stay carefully - camping in the parking spot of Ralphs in Encino? Not a good idea, too many rich people around, means the cops are diligent.

Camping out in Walmart or in the back of strip mall carparks - not such a big deal.

WORD OF WARNING - you are to an extent at the mercy of whichever asshole in a uniform shows up - DO NOT HAVE DRUGS IN YOUR POSESSION. THis can make a "lets roust this johnny-live-frugal out of the neighbourhood" to "cuff him and book him".

My advice if travelling cross country - great to have a sleeper, but also buy a propane stove, some good camping gear, some fold up camp chairs and half a pound of sticky and make the most of the incredible national and state parks. There are many, and they are cheap.

half a pound of sticky?

Marijuana.

Honestly, that would not deter meaning from thinking you might be an eccentric meth head or worse, maybe even bolster the perception.

Any tips on places to car-sleep in Palo Alto? I'm often hacking there late into the night and would appreciate any suggestions.

Get a monthly pass at hackerdojo.

Walmarts and hospitals--I'm going to file this new information away, just in case (you never know where life will take you).

Most Walmarts. For example, the Walmart in Williston ND had to chase everyone away because of all the problems they were having. Boom areas with housing shortages tend to have problems.