So, it's pretty clear that champs in Dominion are not as well balanced as SR.

Is it possible to tweak stats for the game mode - such as base stats, progression, AP/AD ratios? This seems to be the major toolset used in patches.

Why not break dom apart from SR champion stats?

bad idea... almost fully prevents people from playing both modes well. I would rather have 20 champions be necessary bans than have all champions with equal viability and have it be unplayable with my casual SR friends

This is a route that we're currently not willing to take for multiple reasons.
First, it places a huge burden of knowledge on players. AP/AD ratios are already hidden, and making them different on top of that would be very difficult to manage for most players. In addition, it would also effectively mean that an entire layer of new balance challenges would be presented. Rather than going down this route, I would prefer (and will do) a more holistic analysis of why specific champions are imbalanced. For example, if Jax is currently problematic, it's worth realizing that he's also quite strong on Summoner's Rift, so live design may eventually adjust him. Or, if Jax and other champions are hyperscaling towards late game, another fix could be to adjust the experience curve so that Jax (and other champions) take longer to scale to critical mass.

I think balancing through dominion specific items would be a more logical route to balancing out champions. I also disagree that there are balance issues over SR. SR has its own set of champions that are top tier and just because this doesn't align with Dominion's top tiers doesn't mean it has "champion balance" problems. Champions in this game are not balanced. Making it Dominion specific is just foolish. However, changing items (and creating/removing) can allow a shift in the current meta of champions that are in Dominion's top tiers.

Disappointing in this thread, thought this was an @nome in the sense of we ask about him.

Jax scales well mid to late game, but starts weak. Before he gets boots, Sheen, and preferably a Phage, with some ranks of w and preferably his ult, he feels pretty **** UP, to be honest. I don't see that making him take longer to be viable within the match is a good thing. I'd much rather see some late game power sacrificed for a stronger early game, if you want to re-balance.

Perhaps you could adjust Relentless Assault. It seems nearly useless early game, with slow base attack speed and such low speed boost each swing, it rarely gets stacked and when it does, it's not terribly powerful... late game, it's a HUGE boost to his sustained damage that's up QUICKLY. What if it was just a 10% boost per swing capping at 6 stacks at every level, no scaling? It would boost his early game, taking the boost from 24% maximum to 60% maximum AS and stacking noticeably quicker, while lowering his late game, taking the boost down to 60% maximum from the current 84% maximum, lowering his sustained, and to a degree his burst dps from both auto attacks and his ult in end game.

Since we are caught up on Jax, the main issue is that he has a lot of advantages of other bruisers with extra bonuses.

Health - 98 health per level! 12 more than Xin, Yorick, and other similar jumpers. Why is he so freaking tough?!?

Leap - Pretty fast cooldown, 700 range. Better than most.

Dodge - Ability to avoid creep damage when he jumps, letting him ignore creep positioning. Dodges many bruiser Q's (attack resetters).

Mixed damage type - Harder to itemize against, relative to a Riven, GP, Fizz, etc.

High burst damage AND high sustained damage - Has the burst of a physical caster, but the sustain of an autoattacker.

Stun - even vs magic-using enemies, he can pop Counterstrike, Leap, Empower, Counter-stun. Gives him much the same offense style as Pantheon, except with more advantages.

AD AND AP scaling - most are AD only, with just 1 crappy ability that scales with AP, mostly tossed in to prevent too much scaling.

An actual GOOD defensive ult - Compare to crappy Xin's ult that has to hit pretty much ALL the enemies to give him any decent bonus.

This is a terrible idea.

Champ stats should remain constant throughout modes. The only balance changes needed specifically for Dominion are replacing existing SR items with Dominion-only items and tweaking the global aura.