Hey Tom. I'm not sure all polymer products are the same. They all have different tradeoffs in appearance, durability, cost, ease of use, etc. The ultimate goal is to find one with the same tradeoffs that you make. Thus your perfect (but not someone else's) product.
I don't believe any really catalyze in the way paint does. Layering to me is pretty speculative. I actually think a heavy paste wax applied carefully is the most likely to develop a rea film build. Carnauba is very sticky, and pastes are lower in solvents. But that's another story... At the worst, when you apply a new layer, your car just has a fresh layer ready to take on whatever the world throws at it. At best you can build layers infinitely until your car can deflect bullets. I suspect the truth is somewhere in between there.
I think most protectants apply fine by hand, though machine application can just speed it up. Some protectants work poorly by machine because they dry out too fast. Heat would probably not be good for any protectant product as it would flash off the solvents quickly. An orbital buffer would work better for final waxing than a rotary would in most cases. But there are products made extra "wet" for rotary use.
You are right on that prep is key to a great appearance. Wax will pretty much always add some shine, but it won't make a dull car look awesome, just less dull. I'd say the best time to evaluate is after you wash it. The car will be clean and you can touch it, etc. You can also evaluate it after claying. Swirls and such will be there before and after claying, so you should be able to see them either time. Hopefully your claying won't cause any more swirls. Keep an eye on what you are doing and stop if it does. Keep the clay clean, fold it a lot. I cut a bar up into smaller pieces. If the car needs claying real bad, you may go through a couple pieces or the whole bar. Use however much it takes to do it right. Most consumer clay is 80-100g. The Corvette is small. If it were in bad need of clay, I suspect a whole bar would easily be enough. If it's in pretty good shape, you may be able to clay the car 3-4 times with that size bar. I'd cut it into 3-4 pieces if I were you and use one piece at a time.
You are right about polishes/cleaners. More abrasive will work faster/harder and correct deeper imperfections. This is because it will remove more paint. There may be a point where you'd rather leave scratches in the paint than remove that much paint depth. But for hand application, we are talking pretty mild products that won't do much more than correct mild swirls. Chemical cleaners do not have much or any abrasive and work on chemical action. They typically wont' remove swirls as they typically wont' remove any/much healthy paint. They will remove oxidized paint quite easily along with other staining and are good for removing paint transfer (like if someone dinged you or you opened your door into a painted post). Chemical cleaners, in my opinion, tend to be a bit safer to use because they shouldn't leave hazing or marring behind (there are many abrasive swirl removers that also don't leave any hazing/marring too), are awesome on dulling oxidation and embedded dirt/grime. They are just good for what is on most cars.
That said, abrasives will also remove oxidation and such, and will help correct swirls/scratches. In reality most products have both chemical and abrasive cleaning action, just in different proportions, etc to do different jobs. And abrasives can be of differing sizes, can break down more slowly, less slowly, etc. There are a million factors. On the plus side, most products out there are pretty good.
Evaluating your car after the cleaning step will tell you if a chemical cleaner addressed all the trouble spots, or if a swirl remover is needed. And if you used an abrasive, it will tell you if you removed all the swirls you were trying to remove, etc. You should be constantly evaluating your car during the process to see what it needs and what it no longer needs.
In the end, the important thing is to enjoy it, not to get overwhelmed. Whatever combination of products you go with is likely to improve the appearance of your car without causing harm to it. And you'll be more familiar with a set of products and with the process in general so you can make more informed buying/process decisions in the future, or you can decide you've gone as far as you are interested and you can sit back and enjoy a sparkling car.
As an aside, one thing I might suggest is not to go hog wild and buy 20,000,000 things. Good things to buy that you won't regret/never use are great towels, nice applicators, and great wash tools (chenile sponges, sheepskin, whatever your preference...). Then I'd say buy a nice cleaner and a nice protectant, some clay, and go to work. If you Clay, AIO, and SG the car and decide it looks great but there are some swirls you now notice, you can pick up a swirl remover to use the next time. It's up to you, though. To how perfect you want to make the car on the first try, and to how much money you want to possibly waste on products you decide you don't need or on products that after you've used a few you decide aren't the ones you should have bought, etc.
