I understand your attempts to eliminate RNG as much as possible, but I don’t think we should purge all forms of RNG as if it’s the plague or something. I feel like it would be a chore to play a game when everything becomes predictable. I would even argue Duelyst is already consistent enough, with a 5-card starting hand with 2 mulligans and the replacing mechanic. RNG is actually a reason why games are engaging; Hearthstone is based on the same philosophy, albeit it was taken too far.
Before I start rambling off, I do like your changes to Jaxi, Z0r, Lodestar, White Widow, Grimes, Vitriol, and Chrysalis Burst. These changes do not change the card entirely, and still preserves the flavor of the card. Other examples I do not like as much.
First, I think your change to Battle Pets is pretty overcomplicated. The RNG is Battle Pets is inconsistent, but it is an intuitive mechanic. Their randomness is also what makes them unique, and I wouldn’t be so fast to dilute it. An alternative solution is to give Battle Pets unique keywords that make them prioritize a certain target, such as the enemy General or the enemy with the highest Attack.
Your change to Abjudicator feels bad because it will eliminate any reason to play it over Manaforger. I suppose an Opening Gambit is a stronger effect than a passive one, but in terms of spell-based utility, Manaforger will be superior. My solution would be making it lower the cost of a spell in your hand with the highest cost by 1.
Making Bloodsworn Gambler cost 9 may solve its inherent problems, but it just doesn’t feel correct in terms of artistic cohesion. Cards like Worldcore Golem and Grandmaster Kraigon are 9 mana, and it makes sense because they are earth-shattering behemoths. I know balance is important, but I feel like it’s not worth sacrificing this cohesion to pursue one solution. My personal fix to Gambler is to limit the maximum times it can attack. I think 4 times or even 5 times is a healthy number.
I also dislike your change to Blue Conjurer. If I would address its RNG, I would remove certain cards from his card pool that has no application in Vanar decks, such as Nocturne, but that would be it. I would hesitate in weakening his flavor any further. There’s an extent of beauty when playing Blue Conjouer and adjusting your strategy every time you pull a different Arcanyst.
As for Strategos, I would give it the same treatment as Blue Conjurer; removing some cards from his card pool instead of your suggestion. I imagine it would be a near-torture level of boredom to play Strategos be able to predict what cards will promote into what. A solution to both of this issues is to make a token set unique to Strategos, but that’s just unrealistic.
The RNG on Horror Buster feels bad, but your change doesn’t seem like the best answer. I feel like you’re overusing the “nearest unit” mechanic, which is understandable as it’s position-based and thus is interactive, but it’s not a universal solution. An easy fix to Horror Buster is to make it transform a random friendly Wraithling. Simple, intuitive, and not as clunky.
Lastly, while this isn’t RNG related, I’d prefer it if Sunriser stays as it is. You said you wanted Healyoner to be a midrange/control archetype, but that really isn’t a feasible plan if you are taking its win-con away and leaving it no late-game options. As long as you’re not making Excelsious 7 mana or something, it is not a good idea.