Olgar Shiverstone
Legend
Yeah, that's the sort of thing I meant earlier, when I said if I was rewriting the subclass from the ground up, I'd design the beast companion based on the needs of the class, rather than trying to match up with critters in the Monster Manual. I'd still really like to find a solution that doesn't require that, though; hence my being so finicky with this discussion.
Well, then, here's a different idea:
Keep the beast attack as written at 3rd level, where it is a substitute for your attack.
Add in, at, at 3rd level: "As a bonus action, you may direct your beast to take the Disengage or Dodge action. As a bonus action, you may also direct your beast to take the Distract action. With the Distract action, your beast works to distract an opponent within five feet of it, allowing you to make a bonus melee or ranged attack against that opponent with advantage."
That way no matter the fighting style, you get a bonus attack initiated by your beast. The addition of advantage gives everyone, including the TWFer, something they wouldn't have without the beast.
At 7th level: "As a bonus action, you may direct your beast to take the Attack, Dash, or Help action." Now the beast can attack separately, using your bonus action, but without the ranger having to sacrifice an Attack to do so. This isn't quite as good as the 3rd level action, unless the beast's attack is better than your own, or in a situation where having the beast attack is more advantageous.