((P1 + P2) + P2) + ((P1 + P2) + P2) = 100% genotype with double recessive genes for selected trait.
If we strip away all the unnecessary stuff what we really have is a rather quick variation of a back cross, but with a much higher rate of double recessive gene presence and with the need for fewer plants to complete the process.
Many places in the U.S. only allow you to grow 4 plants, some allow 8, some 12, but almost none allow more than that, and most only allow 4.
This cross can be done rather quickly when only searching for a single trait.
The first cross P1 + P2 takes a cycle, The seeds created during cycle 1 are grown and 2 plants from that generation are both crossed back to the parent plant showing the desired double recessive, which can take 1 cycle. Then the seeds from the new generation are grown, selected for the presents of the double recessive and crossed to each other providing both the double recessive in all offspring.
I tried locking in a double recessive trait for purple in a cross of Grape Ape to Mozambique Poison using the traditional method of straight line breeding. Because I was only allowed 8 plants during my cycles, the F2 generation took me 32 plants across 4 cycles to find a double recessive purple plant.
I followed the quicker back cross path on my next project of Grape Ape crossed to Chocolate Thai to lock in a double recessive purple trait, but with the above method I was able to do it in 3 generations, needing to only grow out 24 plants (which could have been done with less). During each selection I focused on the plants most like the Chocolate Thai, but that also held the double recessive purple trait.
I never had the intention of selling any of the seeds I created, it was all done in order to learn more about cannabis breeding. Each new purple strain created still needed stabilized, which I did not do because none of the plants used were truly exceptional. I did grow out 8 plants from the final seeds of each projects, for a total of 16 plants, and every plant was purple.
The one note that I would make is that with this alternate, non traditional, breeding strategy you will end up with a breeding line that is on average 2/3 of the double recessive parent and only 1/3 of the double dominant parent. If you want to have a breeding line that favors all the traits of the double dominant parent line, except the one trait you're trying to secure from the double recessive parent, then traditional line breeding is probably a faster method.
The goal of my post was to provide more methods for breeding, not to provide the "best" method, because the best method depends on the overall goals of the breeder, what traits are being bred for, and what the capacity of the breeder is. If you're capable of growing out a larger number of plants per generation then traditional line breeding is often the better option, but many people who shouldn't be excluded from breeding don't have the option of growing more. This information is to help them!