These changes seem fairly balanced but there are some I have issues with, although most of those issues are more due to personal preference than anything balance related (I like the companion's scaling damage and ridiculous AC).

The only thing that I'd really say is terrible is the changes to Swift Quiver. It is cool that you have changed it so dual-wielders can get the benefit too but you have kind of screwed over Archers in the process. Unless they are using Crossbows with Crossbow Mastery, they can no longer get two bonus attacks as the spell had originally intended and more importantly, they lose the infinite ammunition property of Swift Quiver which imo is far more valuable than the bonus attacks. The latter could be easily remedied by creating a lower level spell that duplicates or creates arrows.

As I already said, my aversion to the removal of the companion's damage and armored AC scaling with proficiency is nothing more than personal preference so I won't comment on that any further. Although I will say that replacing the proficiency damage scaling with ASIs does create some issues within the system. Personally I think it is pretty easy to identify what abilities the companion is using to attack via simple math but not everyone would be able to figure it out so easily and it isn't really that intuitive if you aren't reverse engineering the stat blocks. For example, the Giant Poisonous Snake's Bite attack acts as if it has the Finesse property but the Baboon's Bite does not. The books don't really detail which does or does not have the Finesse property so the players have no reasonable means of knowing which ability they should be increasing in order to increase their companion's damage.

I also think that "One Body" is horrendously OP with its current implementation. If you are mounting your companion (And using the associated feat), your companion doesn't get damaged unless it is via AOE. That equates to the Ranger having a relative HP pool that Dwarfs and humbles the Barbarian in an extreme way. The Ranger would have an effective HP pool of 1D10+1D4+Ranger'sConMod+Companion'sConMod per level which is fairly monstrous and I don't know if it is simply an oversight or not but I really don't think that the Ranger should be the new Tank class.

I'm also not a huge fan of "Coordinated Assault" but that too falls in the realm of personal preference. My only issue with it is the way that ability is worded (A single attack as a bonus action) implies that the Giant Badger is basically screwed. The Badger has been balanced around his Multi-attack and by reducing its effectiveness by 25%, that Giant Badger cannot be balanced with the other CR 1/4 options (Unless WotC didn't do particularly well in balancing the CRs and the Badger is considered more powerful in canon).