I do agree that the Priest, Johktari Beastmaster, and Bloodwave Warlord seem to be in a pretty bad place right now. I think some of the problems are fixable without direct erratas / houseruling, but most of them are not.
Priest:
Yeah, he should definitely either have 10 channeling or not pay 1 mana to place burns (potentially even both). There's just no reason to pick him over the Priestess (for defensive play) or Paladin (for aggressive play) at the moment. Of all the mages, he is consistently the most mana-starved in my experience. If Arcane Wonders ever wants him to be competitive, I don't think there is any way to get around directly altering his abilities (even if only slightly).
Beastmasters:
While your solution does work, I don't think it's actually necessary in the long run. The Straywood Beastmaster is fine as is, and introducing new cards could solve the awkwardness of the combined Sprint and Archery traits. Maybe a card which gives the skirmish trait while attacking with a ranged weapon, or perhaps an enchantment that grants +1 range to attacks. Another option is changing the Sprint ability to allow the Johktari Beastmaster to use a full-action ranged attack after moving twice by deducting 1 damage from the attack for each move action. I kind of feel like a more comprehensive action is needed though. Bows in general just seem really underpowered with every mage due to how restrictive they are. There is an abundance of people running positioning cards like Teleport and Force Push, which probably makes the extra range much less safe than the developers intended.
The other problem with the Johktari Beastmaster, which you didn't address, is her Wounded Prey ability. It sucks. In addition to the +1 damage the creature receives, I would also like it to apply the Lumbering trait, and halve all healing received by the creature (rounded down?). This would make the ability really useful (at least against living targets), let the Beastmaster more easily kite with ranged weapons, and turn her into a mage which specializes in focusing down one creature at a time.
Warlords:
Lastly there are the Warlords. I agree with your suggestion that Battle Orders should be free to cast (once per round). I kind of wish the 2 Warlords' Battle Orders were more differentiated from each other (Bloodwave should be way more offensive than Anvil Throne), but that is hard to fix at this point without completely redoing them. Unfortunately, there is almost no way to make the Bloodwave Warlord equivalent to the Anvil Throne Warlord without some sort of errata or houseruling. The Runesmithing ability is just so good, while the Veterans ability is terrible. I suggest keeping the limitation that veteran tokens cannot stack (to dissuade the Warlord from buddy build strategies), but instead change the ability to read as thus: "Whenever an enemy creature is destroyed, you may choose up to 3 friendly soldier creatures within 1 zone of that creature and give them a Veteran token (maximum of one token per creature). Creatures with a Veteran token gain melee +1, ranged +1, and armor +1." This would make the Warlord's goblin and orc armies a lot more viable (arena-wide buffs to goblins would also help; [mwcard=MWBG1C04]Slaknir, Goblin Chieftain[/mwcard] was a good start but more is needed. The change would also mean players are no longer punished for killing creatures with their mage or playing ranged units (who beforehand gained little benefit from becoming veterans).
Some of these changes might need a bit of tweaking, but I think they are a step in the right direction. In general:
1. the priest needs more mana efficiency (as well as access to more spells which the Paladin cannot as easily use)
2. the Johktari Beastmaster needs better incentives to stay at range, needs to be able to kite creatures effectively, and needs to just generally be less awkward to play
3. the Bloodwave Warlord needs a better primary ability