I'm not saying this is the "right way" to do it, but I've bought 3 vehicles from private sellers, and always driven them home with valid insurance I bought when I was sure I was getting the vehicle, and the seller's tag. Never got pulled over, but I don't get pulled that often anyway.

As to the licenseless thing--one time, on a road trip to New Orleans, I lost my tag 150 miles out from Tampa. I got a license-sized piece of cardboard, wrote "lost tag" and my tag number on it, bolted it where the plate goes, and did the rest of my 5-day, 1500 mile round trip without problems.