Not quite the same--as my move back to the US was from Canada and there were no flights involved--but the moving company was clear regarding the customs forms that all household goods, regardless of when bought, were duty-free. We filled out the forms accordingly.

When we drove across the border before our goods did, Customs didn't ask about anything (including the questions about currency, tobacco, or liquor). In fact, it was up to us to even mention needing their signatures to import our car (which we were driving in). Our goods arrived just fine and on time later.

Your moving company was wrong. The 1-year requirement is there but usually only enforced when people move back and have all new stuff. Alcohol and tobacco is usually only a target if in quantity and especially if coming from a country where it is considerably cheaper.