As a chemistry teacher, I am somewhat horrified at how little grade 11 chemistry some people know.
To answer a few questions.
Do propane and butane mix? Yes, they are fully miscible in their liquid phases.
Does the propane actually burn off first? Kinda. The amount of vapour that comes off a liquid is dependent on the vapour pressures of its component parts. Since the vapour pressure of propane in a propane/butane mixture is higher than the vapour pressure butane, the vapour coming out of the tank has a higher proportion of propane, causing the butane percentage in the cannister to rise.
This is akin to distilling alcohol, where the alcohol leaves the water in a vapour, allowing it to be condensed.
What happens when I turn my cannister upside down? The butane comes out as a liquid. Liquids can't burn, but they always produce a vapour above them, that can. To truly work well, the stove has to have a method of using its heat to convert the liquid to a vapour at some point. That's why turning the canister upside down is less effective on stoves without a pre heater.
How does the propane exist in the cannister? As a liquid. There are two ways to make a gas turn into a liquid, lowering the temperature or increasing the pressure. How much the pressure has to increase is dependent on the boiling point. Since propane has a lower boiling point, it must be under much higher pressure to become a liquid. That's why pure propane cannisters have thicker walls than prop/but mixes.
Keep in mind, most fuels are just a chain of carbons (with hydrogen). Natural gas has one carbon, propane 3, butane 4 and gasoline theoretically 8. Diesel has 10. White gas (coleman fuel) has 6. Ashphalt has about 16. The more carbons, the more difficult it is (the higher the temp required) to convert it to a gas.
Stoves come in two basic designs, ones that assume the fuel is a gas, and ones that assume the fuel is a liquid that must be heated to make a gas. That's why liquid fuel stoves tend not to be finicky about what they burn.
As for the op's question, what he is doing is dangerous. How dangerous, I don't know. If I was doing it, I would sacrifice a couple canisters on a test. Fill the canister with propane, using your method. Find an open area a long ways from civilization. Place the canister in a bucket of water. Place a digital thermometer in the bucket of water that records maximum temp. Place the bucket on another camping stove and heat. Record the temp that the explosion occurs at. If it doesn't explode under the boiling point of water, it's probably safe.
One problem with propane is that when mixed with air, it forms an explosive mixture at a large gap of percentages. That means that exploding propane tanks tend to ignite, while exploding butane tanks don't. It means that if your canister explodes, it will create a fireball. A big one.