Gangplank: I think 1/s is fine for Dominion. I haven't tested him in HA yet.
Thresh getting souls over time: Agree. Return the ratio to 1x (or maybe even 0x, although Souls are rather iconic for him) and give him some stacks over time.
Garen should also get stacks over time. Maybe remove the stacking from kills and just give him stacking over time.
Sion health over time? Sure, but make sure to not overtune it, or else you might turn him into a super-scary beast of a champion. Maybe 1 hp per 5 seconds, giving him 12 hp per minute, 120 hp after 10 minutes, 240 hp after 20 minutes, but reduce the hp on kill to 1 (to prevent farming) and hp per champion kill to 5 (to prevent heavy snowballing). Or just remove the scaling from farm and champion kills and just give him hp over time. It would make him a bit stronger overall, without making him overpowered.
Nasus? The problem with Nasus is that he's horribly designed and not very fun to play against when ahead. Let him remain weak in Dominion until they rework him, not much reason to buff such a toxic champion.
One solution is to slightly buff him without making him overpowered. He might still be unviable, but at least he'd be able to contribute to jungle fights instead of being forced to farm for his stacks. Remove his stacking from Q kills and give him 5-7 stacks per minute (assuming 20 cs, this would be a pretty noticable buff for top lane Nasus, especially considering that you now don't have to farm. He'd still be toxic though).
Cassiopeia: Cassiopeia should have a decent shot at reaching 250 stacks late game, although she's not even that bad right now. Grant her a small increase in scaling, perhaps? Perhaps another 2-3 stacks per minute?
Veigar: Veigar is still quite toxic, due to his incredible burst. I'd be tempted to remove his AP gain from farming altogether and just give him some AP over to compensate/slightly buff, at least that way he won't get basically double the gold value per kill (5 AP is worth a bit more than 100 gold). Something like 3-5 AP per minute might be reasonable. Generally in Dominion, you can expect something like 20 cs, so this would be a nice buff for him.
Bard: Improve his passive.
I generally don't like stacking mechanics that rely on farming, since I believe too many people spend too much time farming and not enough time establishing jungle control or ganking bot. Moving from stacks from minions to stacks over time helps people focus less on farming and more on making plays that win the game.