I am about to playtest the following re-write to the Ranger and Beastmaster in my game,
I've run the 'whiteroom' maths and it all seems fine to me.
I have been allowing the Chain Warlock in the group to command her Pseudodragon in the same way and it's been working fine so far to 4th level.
Anyway, here's the variant, and thereafter, a breakdown of HP progression for a Wolf companion as an example;
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RANGER
Primeval Awareness
Beginning at 3rd level, you can use your action and expend one ranger sell slot to focus your awareness on the region around you. For 1 minute per level of the spell slot you expend, you can sense whether the following types of creatures are present within 1 mile of you: aberrations, celestials, dragons, elementals, fey, fiends and undead. If the region you use this in is your favoured terrain, you may sense these creatures further away, and know whether they are ‘near’ (within 1 mile) or ‘far’ (up to 6 miles).
If one of the creatures you detect is currently the subject of the Hunter’s Mark spell cast by you, you sense the direction in which the creature lies. Otherwise, this feature doesn’t reveal the creature’s location or number.
BEASTMASTER SUBCLASS (Variant)
Ranger’s Companion
At 3rd level you gain a beast companion that accompanies you on your adventures and is trained to fight alongside you. Choose a beast that is no larger than Medium and that has a challenge rating of 1/4 or lower. Add your proficiency bonus to the beast’s AC, attack rolls, and damage as well as to any saving throws and skills it is proficient with. Any abilities the companion has which require a saving throw gain a bonus to their DC equal to half of your proficiency bonus. The beast is strengthened by your special bond with it, starting with maximum HP for its HD and adding your proficiency bonus at 4th level to its HP maximum, and the proficiency bonus again at each new level thereafter.
The beast obeys your commands as best it can. It takes its turn on your initiative, though it doesn’t take an action unless you command it to. It will however defend itself if attacked until next commanded. On your turn you can verbally command the beast to stay put, or where to move (no action required), otherwise the beast will attempt to stay adjacent with you as you move, independently taking the Dash or Disengage actions as necessary to do so.
You can use an action to verbally command it to take the Attack (against specified target), Dash (to specified location), Disengage (to specified location), Dodge, or Help (you, or a known ally) actions. The beast will continue to carry out the last command you gave it until it is no longer relevant or possible, at which point it will return to your side as quickly as possible, independently taking the Dash or Disengage actions as necessary to do so.
Once you have the Extra Attack feature, you can make one attack yourself when you verbally command the beast.
While travelling through your favoured terrain with only the beast, you can move stealthily at a normal pace.
The beast heals during Short or Long Rests as per the rules relevant to the campaign, spending HD equal to its normal total, or half your character level, whichever is highest. If the beast dies, you can obtain another by spending 8 hours magically bonding with another beast that isn’t hostile to you, either the same type of beast as before or a different one.
When you cast the spell Hunter’s Mark, you must choose whether the spell benefits you or your beast companion.
Exceptional Training
Beginning at 7th level, on any of your turns when your beast doesn’t attack, you can use a bonus action to command the beast to take the Dash (to specified location), Disengage (to specified location), Dodge, or Help (you, or a known ally) action on its turn.
Bestial Fury
Starting at 11th level, when you command your beast companion to use the Attack action, it can either make two attacks, or will instead use the Multiattack ability if it is capable of it.
Share Spells
Beginning at 15th level, when you cast a spell targeting yourself, you can also affect your beast companion with the spell if it is within 30ft of you. Hunter’s Mark now benefits both you and your beast companion.
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Wolf Companion HP using variant Beastmaster rules.
Level HP
3 18
4 20
5 23
6 26
7 29
8 32
9 36
10 40
11 44
12 48
13 53
14 58
15 63
16 68
17 74
18 80
19 86
20 92
Feedback would be appreciated...
In my opinion those changes make it actually worth considering playing. haha.
As an alternate suggestion to make Primeval Awareness the slightest bit of use; I had the idear that they spend the spell slot like normal and then get to make a survial check to see if they can locate the critters. And if they were the target of the rangers' hunters' mark the ranger would make the roll with advantage. Set it against a high-ish DC like 20 or so; so that there's at least a chance for the ability to be of any use. haha.
And I agree that the animal companion needs to get progressively tougher otherwise it'll get capped and the ranger will be hosed until it can be replaced. All n all, I like what you got there. 
I'll houserule primeval awareness in my game given the direction, not location or number. I think it's too weak. Instead "look, we have dragons here" we'll have "look, there are dragons in north".