Beastlords are a cool class that doesn't really require much to be fixed. They have unique and desirable utility through cunning, savagery, and their pet stance which is useful on specific fights. I think there are two main issues: their pet, and their lack of scaling dps. I like the idea of making the pet AE/WW/PS immune. I also think the runic pet needs a 20-50% dps boost, since right now it is mostly just a hp upgrade to the previous pet. For comparison, a mage pet can do almost twice as much damage. A pet in-between the level 63 and runic wouldn't hurt as a goal for solo/duo/casual raid player who has had the 63 pet forever.
Scaling dps could be added through meele mechanics, but I much prefer the idea of adding it through spells. Consider adding just two spells to the BST line, replacing Rage of the Wild and Plague.
Hunter's Mark: 350 mana / 1 sec cast / 10 tics / 200 damage on hit and 150 damage per tic / increases the damage dealt by all beastlord pets by 15%
Vulnerability Poison: 550 mana / 2 sec cast / 4 tics / 500 damage on hit and 250 damage per tic / grants all beastlord pets a bonus 30% crit chance.
These spells would by synergistic with beastlord pets and give the beastlord the ability to burn during crucial phases. Hunter's Mark would be the standard, used all the time, for its efficiency, and moderate mana cost. During a burn phase though, the beastlord could use Vulnerability Poison as well, doing decent spell damage, while stacking crit on the bonus damage, granting their pet a nice damage bonus, and if they can stack swarm pets ontop of both of these, they should be able to manage dps numbers close to top dps classes, but the mana cost of these, and their swarm pet, is prohibitive enough that even the best geared beastlords would have to pick and choose when to stack up their damage.
I think just adding new, or adjusting the DOTs BST have, so that they provide reliable, scaling dps, as well as a buff to the relic pet/swarmpet survivability (and dps for just the relic pet, swarmpet dps is okay) would make BST a desirable class. You could just make raw damage DOTs, but the numbers would need to be a lot higher than I listed in that case (beastlords realistically need a 300-400 dps upgrade at the endgame).
Another idea that is a bit more off the wall would be to give BST the WW stance monks lost, and allow it to apply to their pet/swarmpets as well. This would give BST a neat niche with AE dps since they will likely never see the single target DPS of other classes. I think it kind of makes sense lore-wise for the beastlord and his pack of wolves to be able to tear into a group of monsters, damaging them all at the same time.