Existence of a continuum with NWC1(X) not contained in NBO1(X)

Determine whether there exists a continuum X for which the hyperspace of non-weak cut sets of degree 1, NWC1(X) = {A in 2^X : A = X or X - A is 1-Q2}, is not contained in the hyperspace of sets that do not block opens of degree 1, NBO1(X) = {A in 2^X : A = X or X - A is 1-Qo}. Equivalently, ascertain the existence of a closed set A subset of X such that X - A is 1-Q2 but X - A is not 1-Qo.

Background

The authors paper hyperspaces of closed subsets whose complements have specified connectivity degrees. For n=1, NWC1(X) corresponds to sets whose complements satisfy 1-Q2 (non-weak cut sets of degree 1), and NBO1(X) corresponds to sets whose complements satisfy 1-Qo (do not block opens of degree 1).

They present examples showing that NBO1(X) need not be contained in NB1(X) and that NWC1(X) and NBO1(X) can be unequal. However, whether NWC1(X) fails to be a subset of NBO1(X) for some continuum remains unresolved.