Last year I got a bunch of tulle fabric, cut out squares and tied them over individual blossoms. It worked but it was a pain in the butt since pepper flowers are so small (it wasn't as bad on the tomatoes).
I had to look up orgnaza to figure out it's a wedding favor mesh baggie. Those would work as well. Once the flower has been pollinated, you can take off the protection, just mark the peppers that were inside so you don't eat them and save the seeds from the next pepper over.
I save my pepper seeds inside the peppers, which go dry and crispy but last for well over a year with the seeds still viable. I usually have so many seeds that I simply plant the whole old peppers. It's not the most space efficient way of doing things but it does avoid mixing up varieties. What are the advantages of isolation cages/bags? I have never heard of them.
Saving them in the peppers sounds like a great way to store them if the peppers get really crispy dry.
The cages come in when you want to avoid cross-pollination from other nearby pepper varieties. If you have a bell pepper growing next to a jalapeno, there's a decent chance they will be promiscuous and either plants' seeds will be a hybrid (small bell with some spice). My seed saving book says you need 500' of separation between varieties if you aren't caging them. My garden isn't that big Instead of caging the whole plant, I try to just bag a few blossoms and then save seeds from those fruits.
There is a way to look at a plant's flower and tell if it is a self pollinator or if it requires a helper organism.
Look at the flower's structure, if the pollen anthers are above the tip of the pistil, then most likely the plant can and will self-pollinate, if the anthers are below the tip of the pistil then the plant uses pollinators to get the job done.