Edit: Thank you for the nicely done.
I'm going to pick a nit or two here.
First, I have no problem with how you look at it. None.
What needs to be thought of is, what is the purpose of the cross? To sell seed as a hybrid? Oh no, not at all. The only thing you would use from these plant for the next several generations would be the fruit. Then what you propose wouldn't work. You'd need a male sterile line or a self sterile line of peppers for it to work. I don't know of any, but if they exist, then what you propose would work fine, provided you save the seed from only the male sterile plants, as you know they are the hybrid seeds.
If the point is to bring genes in from one plant to another, like you want to create a mustard brain strain, then doing the hand cross would work.I agree, but take into account the scale of the procedure, 5 acres. You only need one seed of the F1 cross to get hundreds if not thousands of seed of for the F2 generation. Grow as many F2s as possible and select out of those the ones that best meet your intended goal. Grow as many seeds as possible from that plant (or plants) and select the best from those, etc. With any luck in 8 or 9 generations you will have a stable new variety. You can up your chance, by doing back crosses, but once you've got the pheno type you want, you still need 8 or 9 generations to get a stable variety. I won't go into the concept of homozygous fatal genes, which can mess up an idea of a variety big time.
Finally, I believe that most people here write OP on seeds to indicate that they is no guarantee that a cross didn't happen. Basically they are saying "I didn't go to any extra trouble to insure that the plant did not cross with another pepper." It is a warning that you might get something different, and that is fine with me. Now if the seeds were from a business, then it wouldn't be ok. Unless they were selling it as an unstable variety and if so, they need to state that explicitly.
Finally yes, you can have F2 seed that is OP. F2 to is just the generation of the seed down from the original cross. Once you are past the F1 generation seed all bets are off. Even if the plants were isolated, so they self pollinated, there are genes still segregating and combining. Look at the SBP7 and how many different pheno types came out of it. That is the whole point of selecting out of hybrids. To make new varieties.
End lecture.