K-formality of connected subgraph arrangements

Prove that every connected subgraph arrangement is k-formal for every k.

Background

The paper proves that every connected subgraph arrangement is combinatorially formal and recalls that free arrangements are k-formal for all permissible values of k. It also cites evidence showing k-formality for all connected subgraph arrangements of rank at most 4 and for all free members of the class. The remaining general assertion is formulated as a conjecture.