I think that restructuring is almost certainly the best overall option. Even if there are other complications, you're going to fight the data with its current structure. Personally, all other things being equal, I would tackle it with Tableau Prep Builder.
However, if it truly isn't an option for you, then the other alternative I see is creating a parameter with an option for each question. That would allow you to swap out the field based on the parameter selection with a calculation, e.g.:
WHEN 1 THEN [Q1]
WHEN 2 THEN [Q2]
Hope that helps!
Agree with Joshua. A vertical structure for survey data is the best way to go. You can pivot your data directly in Tableau as well: Pivot Data from Columns to Rows - Tableau
Admittedly I'm not entirely sure what happens if you add new questions, however.