If Jefferson isn’t the White Rabbit, but, knew the WR from being in Wonderland, wouldn’t the WR have been able to get Jefferson out of Wonderland?
Or, even get Cora out of Wonderland, for that fact.
That’s why Jefferson was stuck in Wonderland, and why Cora wanted him to make another hat….so she could get out of Wonderland because there was no other way besides Jefferson’s hat.
Making the WR another character that could go between worlds provides another way out of Wonderland, therefore undermining the fact that Jefferson and Cora were stuck there.