I hate to say this, but in being able to do that will cause serious repercussions in the form of a lot of nerfing and rebalancing to a point where going from one map to the other even in PVE will only result in a change of scenery.
Is that what you really want?
I know of the unique dogs you speak of.
What good is eldarium if it’s been nerfed to a point that it is no better than starmetal?
What good is unique armors if they’ve been downgraded to the equivalent of epics in the Exiled Lands even when fabricated by a T4 named specialist thrall? This would be just as true with epic and unique weapons.
This is just the tip of the iceburg.
This would be a forced consequence across all servers and include private servers as well as affect solo play. Nobody would be immune to it, regardless of your playstyle or preferences.
I am aware of the loopholes with how to get named thralls and pets to the exiled lands.