I think the 'AvP' movies are more or less their own separate Universe, now.
According to Wikipedia they have a seperate page called "The AVP franchise" and even designated the original Paul W S Anderson AVP logo as the "franchises" identity seperate from ALIEN, PREDATOR.https://en.wikipedia.org/wiki/Alien_vs._Predator
Not sure who sanctioned this or felt they had a position of authority to declare it.
As far as your "THEM!" idea for ALIENS VS PREDATOR 3 I just don't buy it.
Imo this is why I disliked the "plot/setting" for AVP and AVP-R. It inferred the PREDATOR had the Xenomorphs under control. Whereas ALIENS- BOOK ONE (comic graphic novel) by Mark Verheiden was more accurate in the implications of ALIENS on earth.
Also it pissed on the whole point of the Ellen Ripley fears of a Xenomorph getting to Earth and wiping out civilisation. And we know escape ships wouldn't be the answer leaving an infected planet as ALIEN attested.
As littlejimmy said in his AVP (2004) review saying "(In AVP-2004) ALIENS have been depicted being on earth for thousands of years and nothing bad ever came of it". So it makes the whole actions of Ripley (including sacrificing herself in ALIEN 3) seem pointless.
Heck Sigourney Weaver admitted she made ALIEN 3 for two reasons
a- she didn't want ALIENS on a futuristic Blade Runner style Earth setting, claiming it would be boring.
b- she absolutely hated the idea of PREDATOR in an ALIEN movie.
Considering 20th Century Fox had designs on both (proved by News articles I still have in my ALIENS UK magazine) it all makes sense now.
Rather than keeping the plot and setting down. Just make it in a far corner of futuristic space, seperate company from Weyland.