Hi and Welcome
Between the HB6, HB4, and the HB3 for the ATX, my vote goes to the HB6. HB4 is not a bad cartridge and I do get a nice shave with it, I just like the shave I get with the HB6 a little more. Personally, I don’t like using the HB3 Blades with the ATX. It's a good blade but The Headblade Sport adapter is needed to fit it to the ATX razor. For me, I find that it rests lower than what I’m comfortable with.
I love my headblade atx. Though, I do feel that the shock absorber like adapter that can make it a little more of a forgiving razor can also make it not shave as close on the back of my head … specifically the nape area.
While it’s probably not recommended, one of the (probably bad) habits I’ve been getting into is resting my thumb along the edge of the blade cartridge. For me this minimizes the flexing of the adapter and allows me to shave the back of my head a little closer.