Worrying about BM DPR + AC DPR > average character DPR is leading you astray, and will never result in a viable pet.
Since there's two of you, to be "balanced" both characters needs atrocious DPR. Which makes no goddamn sense for a fighter-y character with a melee brute of a beast!
At the very least let's compare to top DPR, not average DPR. Since that's roughly twice as much, it at least gives use leeway for decent DPR for both master and pet. After all, you're bring with you this second entity, that's generally a liability. (And why bring it along if it makes no difference? If you could just be a Hunter Ranger, and be just as effective, I mean. No, if we don't consider it "unbalanced" to buy a war dog or to contract a company of Veterans, we can't keep the weird viewpoint that the Animal Companion must be a zero sum game! It's supposed to be the archetypal "bring a friend" subclass, goddammit! If it doesn't actually add anything, then it's mostly just adding a weak link in the party's chain, and everybody's better off booting it at asking the player to respec. Thus, spotlight!)
And again: don't forget that the pet knows only melee. At high levels, damage generally balloons - doing 1 point of damage simply isn't very valuable any more.
But what I'm most concerned about is defense. The PHB is so utterly pathetic I hesitate to draw any conclusions from it. That is, yes, you can analyze the PHB and say "the pet is basically meant to die, a lot". But that's backwards thinking.
I think a large portion of Beastmasters want one and the same beast to adventure with them for their whole career.
Having to continuously resurrect their beloved companion is an ugly band-aid for the real solution: make it so the pet doesn't die significantly more often than any other party member.
I note you haven't committed to any AC or HP, you just say we have "known numbers". I don't know what that means, but feel free to direct me to a specific reference, or better, just tell me the numbers.
As for pets with different foci, I'm all for that. But the first order of business must be to settle on a reasonable "simple" pet, one that acts as a melee bruiser.
(After all, abilities like fly or scent are almost nothing at high level. Any exploratory abilities are best brought by the ranger, not the pet - at least assuming we're sticking with non-magical beasts)
Zapp
PS. One more thing, that I don't want to devote a whole post for: Oh no, not the "equal pillars" myth again.
Look at the amount of rules for each pillar, Sacrosanct. Look at the actual content of any published official adventure module.
They may say the game is about all three pillars equally, but what that means in practice is 80% combat, 5% exploration, 5 % social and you can distribute the remaining 10% to suit your play style.
Few if any scenarios are meaningfully derailed or delayed by lacking in exploration. There's not even one relevant social challenge that can't be short-circuited by a Charm Person spell (or combat) per scenario on average!
Perhaps you meant that YOU play 33%, 33%, 33%? Because that's something different.
Just let the equal pillars fantasy rest. It's just cakeism from WotC, to borrow a brexism.
In this context, I can only read you bringing up "three pillars" to mean one thing: "the pet needs to easily die each and every time, and that makes for a better game". That's trolling the thread imo. I'm in this thread precisely because I'm trying to make a point: that the fact the pet deserves to be viably sturdy makes the Beastmaster subclass require more than its fair share of spotlight, and that should be the starting position of its design. Therefore your POV is antithetical to mine, and I won't address you further on this subject.
Tl;dr: If you're happy with the PHB Ranger, excellent - stay with that, and have fun! But I'm not.