I read this and a couple things concerned me
A little background, I've hauled it all, cars, trucks, wrecks, tractors, hit air balloons, incomplete major components all on flatbeds, thousands of loads over the last 20 years.
in California the vehicle code requires a minimum of 4 independent anchors, so no sharing a D ring or tying 2 straps to the same point in the load (vehicle)
Chain VS strap is a moot point, truckers use both and 80,000# trucks can tie a 25 ton load down with nylon a little jeep will do fine.
Make sure your chain or strap is heavy enough that each individual strap can hold the weight of the entire vehicle. If it is damged don't use it, I carry rags and place them over any sharp corners the strap may contact.
Frame vs axle...
use one OR the other, do not mix and match. To the axles let's the body bounce a little, if you have soft springs this could be a problem, mix and match is a great way for things to come loose.
I always put all 4 in snug, vehicle in neutral, cinch all straps 2-3 times each, vehicle back in park, frame or axles, get it tight!
Make sure you have solid anchor points on both ends
I generally run straps from the axles out at a slight angle to add tension, I criss cross from time to time as a last resort, and crew cabs on my 20 foot trailer get tied to the center, don't ever go straight down, this allows for vehicle movement.
I have never used webbing that goes over the tire, never had the need.