I agree this is a Hoffman v Zaitsev elimination question. I also understand the kind of thinking being applied to this question. As I think about these reactions, I prefer to further delineate concerted reactions. If time could be infinitely divisible, then no two events could occur at exactly the same time, one will always occur befor the other. If this were so, the E2-elimination reactions may be SN1-like (Zaitsev) and SN2-like (Hoffman).
If you accept this concept, then we can analyze whether the reaction is going to be more SN1-like or SN2-like. The classic Zaitsev products are often found with NaOEt/EtOH. I'd argue these are SN1-like conditions in which the C-X bond lengthens and begins to break. At the same time, electrons from a tertiary center begin attraction, increase acidity, and favor Zaitsev product formation.
Hoffman reactions then favor a semi-initial deprotonation of the most acidic hydrogen and give Hoffman products. I say semi-initial as no anion is formed by deprotonation, simply that hydrogen acidity is a factor leading to product.
Are these conditions SN1-like or SN2-like? Will it give Hoffman or Zaitsev products?