No, Dominion specific nerfs are NOT a good solution.
From a user perspective, say there are players who want to play both modes, and have a favorite champion. It becomes very frustrating for the player to have that champion feel and play differently in one mode to the next.
The items, and Dominion buff aura are the areas that should be tweaked, if any. They need to be global changes to Dominion mechanics, not champion mechanics. A global movespeed cap is an example of that.
Also, to clarify what I mean by item tweaking, I don't mean specific item changes just for Dominion. If a particular item is causing an issue (like Bloodthirster or Warmog's) lock it out and create an appropriate replacement. Again, this keeps the user experience consistent between the game modes.
Poppy is really the perfect example, so I'll expand there a little: in SR, her almost complete inability to lane well makes her a risky pick at best, and a liability at worst. In dominion, the lack of a laning phase makes her a monster. If you buffed/changed her to maker her more viable in SR (gave her some form of sustain, for example), she would be unbelievably broken in Dominion. But any changes to her hyper-carry status in Dominion (passive nerf, ultimate cd increase, etc) would make her utterly trash in SR. Maybe you could tinker with the dominion aura until all 90 or so champions are balanced between the two maps, but I can't see it happening.
The other promising venue is dominion-specific items, but I don't see this bridging the fundamental gap between the two maps (one heavily favors lanining ability, the other teamfighting and mobility).