Ok, should we call it Roux2? That's the most accurate (after maybe Roux and calling Roux Roux2 depending on what came first). But if we talk about the 'rediscovery' of CP first, I would argue that Briggs is the first method that actually made the intellectual leap of CP during FB. The original proposal wasn't necessarily refined but neither was CFOP or any other good method. Also, there have been people who did CPFB in inspection using the 2GR system btw. Anyway, I would think that Briggs with YruRU style CP is the best way to describe your idea, which, as I've said before, is a pretty cool thing to come up with, but it's certainly no different to Briggs as far as the 'method' construction goes.
Also, TIL that people have come up with things such as pEO in the past.
So, this 'method' is Briggs with YruRU style CP. You can do Briggs with 2GR style CP. You could also do it with the bad comm CP thing which was pretty cool for its time. Basically, whatever it is, as long as it follows CPFB, EODFDB, RB, 2GLL you are doing Briggs. A recognition system does not denote a new method. That would mean that there are about 5 different methods that all end with ZBLL for example; that would be absurd. Instead you look at the pieces that are solved in the step (CPFB) and then voila, same method.
Briggs with YruRU style CP, the best way to describe the method.